X^2+15=18x

Solution for X^2+15=18x equation:

X^2+15=18X

We move all terms to the left:

X^2+15-(18X)=0

a = 1; b = -18; c = +15;
Δ = b2-4ac
Δ = -182-4·1·15
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{66}}{2*1}=\frac{18-2\sqrt{66}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{66}}{2*1}=\frac{18+2\sqrt{66}}{2}
$