5(x-7)(3x+8)=0

Solution for 5(x-7)(3x+8)=0 equation:

5(x-7)(3x+8)=0

We multiply parentheses ..

5(+3x^2+8x-21x-56)=0

We multiply parentheses

15x^2+40x-105x-280=0

We add all the numbers together, and all the variables

15x^2-65x-280=0

a = 15; b = -65; c = -280;
Δ = b2-4ac
Δ = -652-4·15·(-280)
Δ = 21025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21025}=145$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-145}{2*15}=\frac{-80}{30}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+145}{2*15}=\frac{210}{30}
=7
$