18x^2=18x+81-0

Solution for 18x^2=18x+81-0 equation:

18x^2=18x+81-0

We move all terms to the left:

18x^2-(18x+81-0)=0

We add all the numbers together, and all the variables

18x^2-(18x+81)=0

We get rid of parentheses

18x^2-18x-81=0

a = 18; b = -18; c = -81;
Δ = b2-4ac
Δ = -182-4·18·(-81)
Δ = 6156
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:

$\sqrt{\Delta}=\sqrt{6156}=\sqrt{324*19}=\sqrt{324}*\sqrt{19}=18\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{19}}{2*18}=\frac{18-18\sqrt{19}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{19}}{2*18}=\frac{18+18\sqrt{19}}{36}
$