x^2=18x+4

Solution for x^2=18x+4 equation:

x^2=18x+4

We move all terms to the left:

x^2-(18x+4)=0

We get rid of parentheses

x^2-18x-4=0

a = 1; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·1·(-4)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{85}}{2*1}=\frac{18-2\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{85}}{2*1}=\frac{18+2\sqrt{85}}{2}
$