3(2x-5)(-4x+1)=0

Solution for 3(2x-5)(-4x+1)=0 equation:

3(2x-5)(-4x+1)=0

We multiply parentheses ..

3(-8x^2+2x+20x-5)=0

We multiply parentheses

-24x^2+6x+60x-15=0

We add all the numbers together, and all the variables

-24x^2+66x-15=0

a = -24; b = 66; c = -15;
Δ = b2-4ac
Δ = 662-4·(-24)·(-15)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-54}{2*-24}=\frac{-120}{-48}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+54}{2*-24}=\frac{-12}{-48}
=1/4
$