0=h^2+5h-24

Solution for 0=h^2+5h-24 equation:

0=h^2+5h-24

We move all terms to the left:

0-(h^2+5h-24)=0

We add all the numbers together, and all the variables

-(h^2+5h-24)=0

We get rid of parentheses

-h^2-5h+24=0

We add all the numbers together, and all the variables

-1h^2-5h+24=0

a = -1; b = -5; c = +24;
Δ = b2-4ac
Δ = -52-4·(-1)·24
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-1}=\frac{-6}{-2}
=+3
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-1}=\frac{16}{-2}
=-8
$