x2+21x+100=21

Solution for x2+21x+100=21 equation:

x2+21x+100=21

We move all terms to the left:

x2+21x+100-(21)=0

We add all the numbers together, and all the variables

x^2+21x+79=0

a = 1; b = 21; c = +79;
Δ = b2-4ac
Δ = 212-4·1·79
Δ = 125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-5\sqrt{5}}{2*1}=\frac{-21-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+5\sqrt{5}}{2*1}=\frac{-21+5\sqrt{5}}{2}
$