a2-20a-101=-5

Solution for a2-20a-101=-5 equation:

a2-20a-101=-5

We move all terms to the left:

a2-20a-101-(-5)=0

We add all the numbers together, and all the variables

a^2-20a-96=0

a = 1; b = -20; c = -96;
Δ = b2-4ac
Δ = -202-4·1·(-96)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-28}{2*1}=\frac{-8}{2}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+28}{2*1}=\frac{48}{2}
=24
$