4×2+7x=5x-5

Subtract 5x from both sides of the equation.

4×2+7x-5x=-5

Subtract 5x from 7x.

4×2+2x=-5

4×2+2x=-5

Move 5 to the left side of the equation by adding it to both sides.

4×2+2x+5=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=4, b=2, and c=5 into the quadratic formula and solve for x.

-2±22-4⋅(4⋅5)2⋅4

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(4⋅5)2⋅4

Multiply 4 by 5.

x=-2±4-4⋅202⋅4

Multiply -4 by 20.

x=-2±4-802⋅4

Subtract 80 from 4.

x=-2±-762⋅4

Rewrite -76 as -1(76).

x=-2±-1⋅762⋅4

Rewrite -1(76) as -1⋅76.

x=-2±-1⋅762⋅4

Rewrite -1 as i.

x=-2±i⋅762⋅4

Rewrite 76 as 22⋅19.

Factor 4 out of 76.

x=-2±i⋅4(19)2⋅4

Rewrite 4 as 22.

x=-2±i⋅22⋅192⋅4

x=-2±i⋅22⋅192⋅4

Pull terms out from under the radical.

x=-2±i⋅(219)2⋅4

Move 2 to the left of i.

x=-2±2i192⋅4

x=-2±2i192⋅4

Multiply 2 by 4.

x=-2±2i198

Simplify -2±2i198.

x=-1±i194

x=-1±i194

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(4⋅5)2⋅4

Multiply 4 by 5.

x=-2±4-4⋅202⋅4

Multiply -4 by 20.

x=-2±4-802⋅4

Subtract 80 from 4.

x=-2±-762⋅4

Rewrite -76 as -1(76).

x=-2±-1⋅762⋅4

Rewrite -1(76) as -1⋅76.

x=-2±-1⋅762⋅4

Rewrite -1 as i.

x=-2±i⋅762⋅4

Rewrite 76 as 22⋅19.

Factor 4 out of 76.

x=-2±i⋅4(19)2⋅4

Rewrite 4 as 22.

x=-2±i⋅22⋅192⋅4

x=-2±i⋅22⋅192⋅4

Pull terms out from under the radical.

x=-2±i⋅(219)2⋅4

Move 2 to the left of i.

x=-2±2i192⋅4

x=-2±2i192⋅4

Multiply 2 by 4.

x=-2±2i198

Simplify -2±2i198.

x=-1±i194

Change the ± to +.

x=-1+i194

Rewrite -1 as -1(1).

x=-1⋅1+i194

Factor -1 out of i19.

x=-1⋅1-(-i19)4

Factor -1 out of -1(1)-(-i19).

x=-1(1-i19)4

Move the negative in front of the fraction.

x=-1-i194

x=-1-i194

Simplify the numerator.

Raise 2 to the power of 2.

x=-2±4-4⋅(4⋅5)2⋅4

Multiply 4 by 5.

x=-2±4-4⋅202⋅4

Multiply -4 by 20.

x=-2±4-802⋅4

Subtract 80 from 4.

x=-2±-762⋅4

Rewrite -76 as -1(76).

x=-2±-1⋅762⋅4

Rewrite -1(76) as -1⋅76.

x=-2±-1⋅762⋅4

Rewrite -1 as i.

x=-2±i⋅762⋅4

Rewrite 76 as 22⋅19.

Factor 4 out of 76.

x=-2±i⋅4(19)2⋅4

Rewrite 4 as 22.

x=-2±i⋅22⋅192⋅4

x=-2±i⋅22⋅192⋅4

Pull terms out from under the radical.

x=-2±i⋅(219)2⋅4

Move 2 to the left of i.

x=-2±2i192⋅4

x=-2±2i192⋅4

Multiply 2 by 4.

x=-2±2i198

Simplify -2±2i198.

x=-1±i194

Change the ± to -.

x=-1-i194

Rewrite -1 as -1(1).

x=-1⋅1-i194

Factor -1 out of -i19.

x=-1⋅1-(i19)4

Factor -1 out of -1(1)-(i19).

x=-1(1+i19)4

Move the negative in front of the fraction.

x=-1+i194

x=-1+i194

The final answer is the combination of both solutions.

x=-1-i194,-1+i194

Solve Using the Square Root Property 4x^2+7x=5x-5