-6x(4x+1)=-24x-6

Solution for -6x(4x+1)=-24x-6 equation:

-6x(4x+1)=-24x-6

We move all terms to the left:

-6x(4x+1)-(-24x-6)=0

We multiply parentheses

-24x^2-6x-(-24x-6)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-24x^2+18x+6=0

a = -24; b = 18; c = +6;
Δ = b2-4ac
Δ = 182-4·(-24)·6
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*-24}=\frac{-48}{-48}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*-24}=\frac{12}{-48}
=-1/4
$