-5h(h+12)-(4h-2)=h-8

Solution for -5h(h+12)-(4h-2)=h-8 equation:

-5h(h+12)-(4h-2)=h-8

We move all terms to the left:

-5h(h+12)-(4h-2)-(h-8)=0

We multiply parentheses

-5h^2-60h-(4h-2)-(h-8)=0

We get rid of parentheses

-5h^2-60h-4h-h+2+8=0

We add all the numbers together, and all the variables

-5h^2-65h+10=0

a = -5; b = -65; c = +10;
Δ = b2-4ac
Δ = -652-4·(-5)·10
Δ = 4425
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:

$\sqrt{\Delta}=\sqrt{4425}=\sqrt{25*177}=\sqrt{25}*\sqrt{177}=5\sqrt{177}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-5\sqrt{177}}{2*-5}=\frac{65-5\sqrt{177}}{-10}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+5\sqrt{177}}{2*-5}=\frac{65+5\sqrt{177}}{-10}
$