3(4x-5)(2x+7)=0

Solution for 3(4x-5)(2x+7)=0 equation:

3(4x-5)(2x+7)=0

We multiply parentheses ..

3(+8x^2+28x-10x-35)=0

We multiply parentheses

24x^2+84x-30x-105=0

We add all the numbers together, and all the variables

24x^2+54x-105=0

a = 24; b = 54; c = -105;
Δ = b2-4ac
Δ = 542-4·24·(-105)
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-114}{2*24}=\frac{-168}{48}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+114}{2*24}=\frac{60}{48}
=1+1/4
$