H=8x^2+20x+5

Solution for H=8x^2+20x+5 equation:

=8H^2+20H+5

We move all terms to the left:

-(8H^2+20H+5)=0

We get rid of parentheses

-8H^2-20H-5=0

a = -8; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·(-8)·(-5)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{15}}{2*-8}=\frac{20-4\sqrt{15}}{-16}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{15}}{2*-8}=\frac{20+4\sqrt{15}}{-16}
$