3456^2=h^2+24h

Solution for 3456^2=h^2+24h equation:

3456^2=h^2+24h

We move all terms to the left:

3456^2-(h^2+24h)=0

We add all the numbers together, and all the variables

-(h^2+24h)+11943936=0

We get rid of parentheses

-h^2-24h+11943936=0

We add all the numbers together, and all the variables

-1h^2-24h+11943936=0

a = -1; b = -24; c = +11943936;
Δ = b2-4ac
Δ = -242-4·(-1)·11943936
Δ = 47776320
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:

$\sqrt{\Delta}=\sqrt{47776320}=\sqrt{576*82945}=\sqrt{576}*\sqrt{82945}=24\sqrt{82945}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{82945}}{2*-1}=\frac{24-24\sqrt{82945}}{-2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{82945}}{2*-1}=\frac{24+24\sqrt{82945}}{-2}
$