X+3=x^2-9x-18

Solution for X+3=x^2-9x-18 equation:

X+3=X^2-9X-18

We move all terms to the left:

X+3-(X^2-9X-18)=0

We get rid of parentheses

-X^2+X+9X+18+3=0

We add all the numbers together, and all the variables

-1X^2+10X+21=0

a = -1; b = 10; c = +21;
Δ = b2-4ac
Δ = 102-4·(-1)·21
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{46}}{2*-1}=\frac{-10-2\sqrt{46}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{46}}{2*-1}=\frac{-10+2\sqrt{46}}{-2}
$