X^2-7x-18=x

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

X^2-7X-18=X

We move all terms to the left:

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

We add all the numbers together, and all the variables

X^2-8X-18=0

a = 1; b = -8; c = -18;
Δ = b2-4ac
Δ = -82-4·1·(-18)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*1}=\frac{8-2\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*1}=\frac{8+2\sqrt{34}}{2}
$