(x^2)+(6x-45)=90

Solution for (x^2)+(6x-45)=90 equation:

(x^2)+(6x-45)=90

We move all terms to the left:

(x^2)+(6x-45)-(90)=0

We get rid of parentheses

x^2+6x-45-90=0

We add all the numbers together, and all the variables

x^2+6x-135=0

a = 1; b = 6; c = -135;
Δ = b2-4ac
Δ = 62-4·1·(-135)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*1}=\frac{18}{2}
=9
$