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

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

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

We multiply parentheses ..

4(+6x^2+4x-21x-14)=0

We multiply parentheses

24x^2+16x-84x-56=0

We add all the numbers together, and all the variables

24x^2-68x-56=0

a = 24; b = -68; c = -56;
Δ = b2-4ac
Δ = -682-4·24·(-56)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-100}{2*24}=\frac{-32}{48}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+100}{2*24}=\frac{168}{48}
=3+1/2
$