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

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

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

We multiply parentheses ..

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

We get rid of parentheses

10x^2+45x-30x-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{-90}{20}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+75}{2*10}=\frac{60}{20}
=3
$