5x+82=x^2-3x+18

Solution for 5x+82=x^2-3x+18 equation:

5x+82=x^2-3x+18

We move all terms to the left:

5x+82-(x^2-3x+18)=0

We get rid of parentheses

-x^2+5x+3x-18+82=0

We add all the numbers together, and all the variables

-1x^2+8x+64=0

a = -1; b = 8; c = +64;
Δ = b2-4ac
Δ = 82-4·(-1)·64
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{5}}{2*-1}=\frac{-8-8\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{5}}{2*-1}=\frac{-8+8\sqrt{5}}{-2}
$