(x+30)(x-45)=0

Solution for (x+30)(x-45)=0 equation:

(x+30)(x-45)=0

We multiply parentheses ..

(+x^2-45x+30x-1350)=0

We get rid of parentheses

x^2-45x+30x-1350=0

We add all the numbers together, and all the variables

x^2-15x-1350=0

a = 1; b = -15; c = -1350;
Δ = b2-4ac
Δ = -152-4·1·(-1350)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-75}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+75}{2*1}=\frac{90}{2}
=45
$