a^2+2a-72=-5

Solution for a^2+2a-72=-5 equation:

a^2+2a-72=-5

We move all terms to the left:

a^2+2a-72-(-5)=0

We add all the numbers together, and all the variables

a^2+2a-67=0

a = 1; b = 2; c = -67;
Δ = b2-4ac
Δ = 22-4·1·(-67)
Δ = 272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{17}}{2*1}=\frac{-2-4\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{17}}{2*1}=\frac{-2+4\sqrt{17}}{2}
$