2x^2-32x=-60

Solution for 2x^2-32x=-60 equation:

2x^2-32x=-60

We move all terms to the left:

2x^2-32x-(-60)=0

We add all the numbers together, and all the variables

2x^2-32x+60=0

a = 2; b = -32; c = +60;
Δ = b2-4ac
Δ = -322-4·2·60
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{34}}{2*2}=\frac{32-4\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{34}}{2*2}=\frac{32+4\sqrt{34}}{4}
$