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

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

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

We multiply parentheses ..

3(+x^2+5x-7x-35)=0

We multiply parentheses

3x^2+15x-21x-105=0

We add all the numbers together, and all the variables

3x^2-6x-105=0

a = 3; b = -6; c = -105;
Δ = b2-4ac
Δ = -62-4·3·(-105)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-36}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+36}{2*3}=\frac{42}{6}
=7
$