-2x(x+7)=-8-x+12

Solution for -2x(x+7)=-8-x+12 equation:

-2x(x+7)=-8-x+12

We move all terms to the left:

-2x(x+7)-(-8-x+12)=0

We add all the numbers together, and all the variables

-2x(x+7)-(-1x+4)=0

We multiply parentheses

-2x^2-14x-(-1x+4)=0

We get rid of parentheses

-2x^2-14x+1x-4=0

We add all the numbers together, and all the variables

-2x^2-13x-4=0

a = -2; b = -13; c = -4;
Δ = b2-4ac
Δ = -132-4·(-2)·(-4)
Δ = 137
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{-(-13)-\sqrt{137}}{2*-2}=\frac{13-\sqrt{137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{137}}{2*-2}=\frac{13+\sqrt{137}}{-4}
$