h^2+10h-233=0

Solution for h^2+10h-233=0 equation:

h^2+10h-233=0

a = 1; b = 10; c = -233;
Δ = b2-4ac
Δ = 102-4·1·(-233)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{258}}{2*1}=\frac{-10-2\sqrt{258}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{258}}{2*1}=\frac{-10+2\sqrt{258}}{2}
$