(3x-21)(5x+15)=0

Solution for (3x-21)(5x+15)=0 equation:

(3x-21)(5x+15)=0

We multiply parentheses ..

(+15x^2+45x-105x-315)=0

We get rid of parentheses

15x^2+45x-105x-315=0

We add all the numbers together, and all the variables

15x^2-60x-315=0

a = 15; b = -60; c = -315;
Δ = b2-4ac
Δ = -602-4·15·(-315)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-150}{2*15}=\frac{-90}{30}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+150}{2*15}=\frac{210}{30}
=7
$