(4x-6)(-6x-1)=0

Solution for (4x-6)(-6x-1)=0 equation:

(4x-6)(-6x-1)=0

We multiply parentheses ..

(-24x^2-4x+36x+6)=0

We get rid of parentheses

-24x^2-4x+36x+6=0

We add all the numbers together, and all the variables

-24x^2+32x+6=0

a = -24; b = 32; c = +6;
Δ = b2-4ac
Δ = 322-4·(-24)·6
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-40}{2*-24}=\frac{-72}{-48}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+40}{2*-24}=\frac{8}{-48}
=-1/6
$