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

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

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

We multiply parentheses ..

5(+3x^2+7x-12x-28)=0

We multiply parentheses

15x^2+35x-60x-140=0

We add all the numbers together, and all the variables

15x^2-25x-140=0

a = 15; b = -25; c = -140;
Δ = b2-4ac
Δ = -252-4·15·(-140)
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-95}{2*15}=\frac{-70}{30}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+95}{2*15}=\frac{120}{30}
=4
$