x^2+20x+100=156.25

Solution for x^2+20x+100=156.25 equation:

x^2+20x+100=156.25

We move all terms to the left:

x^2+20x+100-(156.25)=0

We add all the numbers together, and all the variables

x^2+20x-56.25=0

a = 1; b = 20; c = -56.25;
Δ = b2-4ac
Δ = 202-4·1·(-56.25)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-25}{2*1}=\frac{-45}{2}
=-22+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+25}{2*1}=\frac{5}{2}
=2+1/2
$