-4x^2+8x=x+2

Solution for -4x^2+8x=x+2 equation:

-4x^2+8x=x+2

We move all terms to the left:

-4x^2+8x-(x+2)=0

We get rid of parentheses

-4x^2+8x-x-2=0

We add all the numbers together, and all the variables

-4x^2+7x-2=0

a = -4; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-4)·(-2)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{17}}{2*-4}=\frac{-7-\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-4}=\frac{-7+\sqrt{17}}{-8}
$