-5w^2+32w=-12

Solution for -5w^2+32w=-12 equation:

-5w^2+32w=-12

We move all terms to the left:

-5w^2+32w-(-12)=0

We add all the numbers together, and all the variables

-5w^2+32w+12=0

a = -5; b = 32; c = +12;
Δ = b2-4ac
Δ = 322-4·(-5)·12
Δ = 1264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{79}}{2*-5}=\frac{-32-4\sqrt{79}}{-10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{79}}{2*-5}=\frac{-32+4\sqrt{79}}{-10}
$