3x^2-12x-32=-3

Solution for 3x^2-12x-32=-3 equation:

3x^2-12x-32=-3

We move all terms to the left:

3x^2-12x-32-(-3)=0

We add all the numbers together, and all the variables

3x^2-12x-29=0

a = 3; b = -12; c = -29;
Δ = b2-4ac
Δ = -122-4·3·(-29)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{123}}{2*3}=\frac{12-2\sqrt{123}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{123}}{2*3}=\frac{12+2\sqrt{123}}{6}
$