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

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

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

We move all terms to the left:

2x+3-(x^2-x-18)=0

We get rid of parentheses

-x^2+2x+x+18+3=0

We add all the numbers together, and all the variables

-1x^2+3x+21=0

a = -1; b = 3; c = +21;
Δ = b2-4ac
Δ = 32-4·(-1)·21
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{93}}{2*-1}=\frac{-3-\sqrt{93}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{93}}{2*-1}=\frac{-3+\sqrt{93}}{-2}
$