X^2-7=18x

Solution for X^2-7=18x equation:

X^2-7=18X

We move all terms to the left:

X^2-7-(18X)=0

a = 1; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·1·(-7)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{22}}{2*1}=\frac{18-4\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{22}}{2*1}=\frac{18+4\sqrt{22}}{2}
$