x^2+11=18x

Solution for x^2+11=18x equation:

x^2+11=18x

We move all terms to the left:

x^2+11-(18x)=0

a = 1; b = -18; c = +11;
Δ = b2-4ac
Δ = -182-4·1·11
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{70}}{2*1}=\frac{18-2\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{70}}{2*1}=\frac{18+2\sqrt{70}}{2}
$