X^2=18x+14

Solution for X^2=18x+14 equation:

X^2=18X+14

We move all terms to the left:

X^2-(18X+14)=0

We get rid of parentheses

X^2-18X-14=0

a = 1; b = -18; c = -14;
Δ = b2-4ac
Δ = -182-4·1·(-14)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{95}}{2*1}=\frac{18-2\sqrt{95}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{95}}{2*1}=\frac{18+2\sqrt{95}}{2}
$