X^2-18x+81=21

Solution for X^2-18x+81=21 equation:

X^2-18X+81=21

We move all terms to the left:

X^2-18X+81-(21)=0

We add all the numbers together, and all the variables

X^2-18X+60=0

a = 1; b = -18; c = +60;
Δ = b2-4ac
Δ = -182-4·1·60
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{21}}{2*1}=\frac{18-2\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{21}}{2*1}=\frac{18+2\sqrt{21}}{2}
$