h^2-28h=9

Solution for h^2-28h=9 equation:

h^2-28h=9

We move all terms to the left:

h^2-28h-(9)=0

a = 1; b = -28; c = -9;
Δ = b2-4ac
Δ = -282-4·1·(-9)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{205}}{2*1}=\frac{28-2\sqrt{205}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{205}}{2*1}=\frac{28+2\sqrt{205}}{2}
$