x^2-6x-32=-7-12x

Solution for x^2-6x-32=-7-12x equation:

x^2-6x-32=-7-12x

We move all terms to the left:

x^2-6x-32-(-7-12x)=0

We add all the numbers together, and all the variables

x^2-6x-(-12x-7)-32=0

We get rid of parentheses

x^2-6x+12x+7-32=0

We add all the numbers together, and all the variables

x^2+6x-25=0

a = 1; b = 6; c = -25;
Δ = b2-4ac
Δ = 62-4·1·(-25)
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{34}}{2*1}=\frac{-6-2\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{34}}{2*1}=\frac{-6+2\sqrt{34}}{2}
$