4t25=3t5+2710

Multiply both sides of the equation by 5.

4t2=3t5⋅(5)+2710⋅(5)

Cancel the common factor of 5.

Cancel the common factor.

4t2=3t5⋅5+2710⋅(5)

Rewrite the expression.

4t2=3t+2710⋅(5)

4t2=3t+2710⋅(5)

Cancel the common factor of 5.

Factor 5 out of 10.

4t2=3t+275(2)⋅5

Cancel the common factor.

4t2=3t+275⋅2⋅5

Rewrite the expression.

4t2=3t+272

4t2=3t+272

4t2=3t+272

Subtract 3t from both sides of the equation.

4t2-3t=272

Move 272 to the left side of the equation by subtracting it from both sides.

4t2-3t-272=0

Apply the distributive property.

2(4t2)+2(-3t)+2(-272)=0

Simplify.

Multiply 4 by 2.

8t2+2(-3t)+2(-272)=0

Multiply -3 by 2.

8t2-6t+2(-272)=0

Cancel the common factor of 2.

Move the leading negative in -272 into the numerator.

8t2-6t+2(-272)=0

Cancel the common factor.

8t2-6t+2(-272)=0

Rewrite the expression.

8t2-6t-27=0

8t2-6t-27=0

8t2-6t-27=0

8t2-6t-27=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=8, b=-6, and c=-27 into the quadratic formula and solve for t.

6±(-6)2-4⋅(8⋅-27)2⋅8

Simplify the numerator.

Raise -6 to the power of 2.

t=6±36-4⋅(8⋅-27)2⋅8

Multiply 8 by -27.

t=6±36-4⋅-2162⋅8

Multiply -4 by -216.

t=6±36+8642⋅8

Add 36 and 864.

t=6±9002⋅8

Rewrite 900 as 302.

t=6±3022⋅8

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

t=6±302⋅8

t=6±302⋅8

Multiply 2 by 8.

t=6±3016

Simplify 6±3016.

t=3±158

t=3±158

The final answer is the combination of both solutions.

t=94,-32

The result can be shown in multiple forms.

Exact Form:

t=94,-32

Decimal Form:

t=2.25,-1.5

Mixed Number Form:

t=214,-112

Solve for t (4t^2)/5=(3t)/5+27/10