h^2+12h=25

Solution for h^2+12h=25 equation:

h^2+12h=25

We move all terms to the left:

h^2+12h-(25)=0

a = 1; b = 12; c = -25;
Δ = b2-4ac
Δ = 122-4·1·(-25)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{61}}{2*1}=\frac{-12-2\sqrt{61}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{61}}{2*1}=\frac{-12+2\sqrt{61}}{2}
$