x+5=x^2-22x-325

Solution for x+5=x^2-22x-325 equation:

x+5=x^2-22x-325

We move all terms to the left:

x+5-(x^2-22x-325)=0

We get rid of parentheses

-x^2+x+22x+325+5=0

We add all the numbers together, and all the variables

-1x^2+23x+330=0

a = -1; b = 23; c = +330;
Δ = b2-4ac
Δ = 232-4·(-1)·330
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-43}{2*-1}=\frac{-66}{-2}
=+33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+43}{2*-1}=\frac{20}{-2}
=-10
$