3(7x-4)(5x+2)=0

Solution for 3(7x-4)(5x+2)=0 equation:

3(7x-4)(5x+2)=0

We multiply parentheses ..

3(+35x^2+14x-20x-8)=0

We multiply parentheses

105x^2+42x-60x-24=0

We add all the numbers together, and all the variables

105x^2-18x-24=0

a = 105; b = -18; c = -24;
Δ = b2-4ac
Δ = -182-4·105·(-24)
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-102}{2*105}=\frac{-84}{210}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+102}{2*105}=\frac{120}{210}
=4/7
$