h^2-3h-27=61

Solution for h^2-3h-27=61 equation:

h^2-3h-27=61

We move all terms to the left:

h^2-3h-27-(61)=0

We add all the numbers together, and all the variables

h^2-3h-88=0

a = 1; b = -3; c = -88;
Δ = b2-4ac
Δ = -32-4·1·(-88)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-19}{2*1}=\frac{-16}{2}
=-8
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*1}=\frac{22}{2}
=11
$