4(5x-3)(3x+8)=0

Solution for 4(5x-3)(3x+8)=0 equation:

4(5x-3)(3x+8)=0

We multiply parentheses ..

4(+15x^2+40x-9x-24)=0

We multiply parentheses

60x^2+160x-36x-96=0

We add all the numbers together, and all the variables

60x^2+124x-96=0

a = 60; b = 124; c = -96;
Δ = b2-4ac
Δ = 1242-4·60·(-96)
Δ = 38416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38416}=196$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-196}{2*60}=\frac{-320}{120}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+196}{2*60}=\frac{72}{120}
=3/5
$