3(x-7)(5x+2)=0

Solution for 3(x-7)(5x+2)=0 equation:

3(x-7)(5x+2)=0

We multiply parentheses ..

3(+5x^2+2x-35x-14)=0

We multiply parentheses

15x^2+6x-105x-42=0

We add all the numbers together, and all the variables

15x^2-99x-42=0

a = 15; b = -99; c = -42;
Δ = b2-4ac
Δ = -992-4·15·(-42)
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-111}{2*15}=\frac{-12}{30}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+111}{2*15}=\frac{210}{30}
=7
$