4(x-6)(-3x-5)=3

Solution for 4(x-6)(-3x-5)=3 equation:

4(x-6)(-3x-5)=3

We move all terms to the left:

4(x-6)(-3x-5)-(3)=0

We multiply parentheses ..

4(-3x^2-5x+18x+30)-3=0

We multiply parentheses

-12x^2-20x+72x+120-3=0

We add all the numbers together, and all the variables

-12x^2+52x+117=0

a = -12; b = 52; c = +117;
Δ = b2-4ac
Δ = 522-4·(-12)·117
Δ = 8320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8320}=\sqrt{64*130}=\sqrt{64}*\sqrt{130}=8\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-8\sqrt{130}}{2*-12}=\frac{-52-8\sqrt{130}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+8\sqrt{130}}{2*-12}=\frac{-52+8\sqrt{130}}{-24}
$