(2h-8)(h-15)=31

Solution for (2h-8)(h-15)=31 equation:

(2h-8)(h-15)=31

We move all terms to the left:

(2h-8)(h-15)-(31)=0

We multiply parentheses ..

(+2h^2-30h-8h+120)-31=0

We get rid of parentheses

2h^2-30h-8h+120-31=0

We add all the numbers together, and all the variables

2h^2-38h+89=0

a = 2; b = -38; c = +89;
Δ = b2-4ac
Δ = -382-4·2·89
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{183}}{2*2}=\frac{38-2\sqrt{183}}{4}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{183}}{2*2}=\frac{38+2\sqrt{183}}{4}
$