(2x-9)(5x+15)=0

Solution for (2x-9)(5x+15)=0 equation:

(2x-9)(5x+15)=0

We multiply parentheses ..

(+10x^2+30x-45x-135)=0

We get rid of parentheses

10x^2+30x-45x-135=0

We add all the numbers together, and all the variables

10x^2-15x-135=0

a = 10; b = -15; c = -135;
Δ = b2-4ac
Δ = -152-4·10·(-135)
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*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+75}{2*10}=\frac{90}{20}
=4+1/2
$