-8(x+1)+x(x-2)=-3x+2

Solution for -8(x+1)+x(x-2)=-3x+2 equation:

-8(x+1)+x(x-2)=-3x+2

We move all terms to the left:

-8(x+1)+x(x-2)-(-3x+2)=0

We multiply parentheses

x^2-8x-2x-(-3x+2)-8=0

We get rid of parentheses

x^2-8x-2x+3x-2-8=0

We add all the numbers together, and all the variables

x^2-7x-10=0

a = 1; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·1·(-10)
Δ = 89
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{89}}{2*1}=\frac{7-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*1}=\frac{7+\sqrt{89}}{2}
$