4t25=7t5+910

Multiply both sides of the equation by 5.

4t2=7t5⋅(5)+910⋅(5)

Cancel the common factor of 5.

Cancel the common factor.

4t2=7t5⋅5+910⋅(5)

Rewrite the expression.

4t2=7t+910⋅(5)

4t2=7t+910⋅(5)

Cancel the common factor of 5.

Factor 5 out of 10.

4t2=7t+95(2)⋅5

Cancel the common factor.

4t2=7t+95⋅2⋅5

Rewrite the expression.

4t2=7t+92

4t2=7t+92

4t2=7t+92

Subtract 7t from both sides of the equation.

4t2-7t=92

Move 92 to the left side of the equation by subtracting it from both sides.

4t2-7t-92=0

Apply the distributive property.

2(4t2)+2(-7t)+2(-92)=0

Simplify.

Multiply 4 by 2.

8t2+2(-7t)+2(-92)=0

Multiply -7 by 2.

8t2-14t+2(-92)=0

Cancel the common factor of 2.

Move the leading negative in -92 into the numerator.

8t2-14t+2(-92)=0

Cancel the common factor.

8t2-14t+2(-92)=0

Rewrite the expression.

8t2-14t-9=0

8t2-14t-9=0

8t2-14t-9=0

8t2-14t-9=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=8, b=-14, and c=-9 into the quadratic formula and solve for t.

14±(-14)2-4⋅(8⋅-9)2⋅8

Simplify the numerator.

Raise -14 to the power of 2.

t=14±196-4⋅(8⋅-9)2⋅8

Multiply 8 by -9.

t=14±196-4⋅-722⋅8

Multiply -4 by -72.

t=14±196+2882⋅8

Add 196 and 288.

t=14±4842⋅8

Rewrite 484 as 222.

t=14±2222⋅8

Pull terms out from under the radical, assuming positive real numbers.

t=14±222⋅8

t=14±222⋅8

Multiply 2 by 8.

t=14±2216

Simplify 14±2216.

t=7±118

t=7±118

Simplify the numerator.

Raise -14 to the power of 2.

t=14±196-4⋅(8⋅-9)2⋅8

Multiply 8 by -9.

t=14±196-4⋅-722⋅8

Multiply -4 by -72.

t=14±196+2882⋅8

Add 196 and 288.

t=14±4842⋅8

Rewrite 484 as 222.

t=14±2222⋅8

Pull terms out from under the radical, assuming positive real numbers.

t=14±222⋅8

t=14±222⋅8

Multiply 2 by 8.

t=14±2216

Simplify 14±2216.

t=7±118

Change the ± to +.

t=7+118

Add 7 and 11.

t=188

Cancel the common factor of 18 and 8.

Factor 2 out of 18.

t=2(9)8

Cancel the common factors.

Factor 2 out of 8.

t=2⋅92⋅4

Cancel the common factor.

t=2⋅92⋅4

Rewrite the expression.

t=94

t=94

t=94

t=94

Simplify the numerator.

Raise -14 to the power of 2.

t=14±196-4⋅(8⋅-9)2⋅8

Multiply 8 by -9.

t=14±196-4⋅-722⋅8

Multiply -4 by -72.

t=14±196+2882⋅8

Add 196 and 288.

t=14±4842⋅8

Rewrite 484 as 222.

t=14±2222⋅8

Pull terms out from under the radical, assuming positive real numbers.

t=14±222⋅8

t=14±222⋅8

Multiply 2 by 8.

t=14±2216

Simplify 14±2216.

t=7±118

Change the ± to -.

t=7-118

Subtract 11 from 7.

t=-48

Cancel the common factor of -4 and 8.

Factor 4 out of -4.

t=4(-1)8

Cancel the common factors.

Factor 4 out of 8.

t=4⋅-14⋅2

Cancel the common factor.

t=4⋅-14⋅2

Rewrite the expression.

t=-12

t=-12

t=-12

Move the negative in front of the fraction.

t=-12

t=-12

The final answer is the combination of both solutions.

t=94,-12

Solve Using the Square Root Property (4t^2)/5=(7t)/5+9/10