0=8h^2+9h-1224

Solution for 0=8h^2+9h-1224 equation:

0=8h^2+9h-1224

We move all terms to the left:

0-(8h^2+9h-1224)=0

We add all the numbers together, and all the variables

-(8h^2+9h-1224)=0

We get rid of parentheses

-8h^2-9h+1224=0

a = -8; b = -9; c = +1224;
Δ = b2-4ac
Δ = -92-4·(-8)·1224
Δ = 39249
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:

$\sqrt{\Delta}=\sqrt{39249}=\sqrt{441*89}=\sqrt{441}*\sqrt{89}=21\sqrt{89}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21\sqrt{89}}{2*-8}=\frac{9-21\sqrt{89}}{-16}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21\sqrt{89}}{2*-8}=\frac{9+21\sqrt{89}}{-16}
$