2x^2-5=132x

Solution for 2x^2-5=132x equation:

2x^2-5=132x

We move all terms to the left:

2x^2-5-(132x)=0

a = 2; b = -132; c = -5;
Δ = b2-4ac
Δ = -1322-4·2·(-5)
Δ = 17464
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:

$\sqrt{\Delta}=\sqrt{17464}=\sqrt{4*4366}=\sqrt{4}*\sqrt{4366}=2\sqrt{4366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-2\sqrt{4366}}{2*2}=\frac{132-2\sqrt{4366}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+2\sqrt{4366}}{2*2}=\frac{132+2\sqrt{4366}}{4}
$