0=4x^2+32x+62

Solution for 0=4x^2+32x+62 equation:

0=4x^2+32x+62

We move all terms to the left:

0-(4x^2+32x+62)=0

We add all the numbers together, and all the variables

-(4x^2+32x+62)=0

We get rid of parentheses

-4x^2-32x-62=0

a = -4; b = -32; c = -62;
Δ = b2-4ac
Δ = -322-4·(-4)·(-62)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{2}}{2*-4}=\frac{32-4\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{2}}{2*-4}=\frac{32+4\sqrt{2}}{-8}
$