H(8h-9)(h+1)=0

Solution for H(8h-9)(h+1)=0 equation:

(8H-9)(H+1)=0

We multiply parentheses ..

(+8H^2+8H-9H-9)=0

We get rid of parentheses

8H^2+8H-9H-9=0

We add all the numbers together, and all the variables

8H^2-1H-9=0

a = 8; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·8·(-9)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*8}=\frac{-16}{16}
=-1
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*8}=\frac{18}{16}
=1+1/8
$