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

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

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

We multiply parentheses ..

4(+3x^2-5x+6x-10)=0

We multiply parentheses

12x^2-20x+24x-40=0

We add all the numbers together, and all the variables

12x^2+4x-40=0

a = 12; b = 4; c = -40;
Δ = b2-4ac
Δ = 42-4·12·(-40)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-44}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+44}{2*12}=\frac{40}{24}
=1+2/3
$