h(h+1)-4=76

Solution for h(h+1)-4=76 equation:

h(h+1)-4=76

We move all terms to the left:

h(h+1)-4-(76)=0

We add all the numbers together, and all the variables

h(h+1)-80=0

We multiply parentheses

h^2+h-80=0

a = 1; b = 1; c = -80;
Δ = b2-4ac
Δ = 12-4·1·(-80)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{321}}{2*1}=\frac{-1-\sqrt{321}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{321}}{2*1}=\frac{-1+\sqrt{321}}{2}
$