-72=3x(-4x-3)-3

Solution for -72=3x(-4x-3)-3 equation:

-72=3x(-4x-3)-3

We move all terms to the left:

-72-(3x(-4x-3)-3)=0


We calculate terms in parentheses: -(3x(-4x-3)-3), so:

3x(-4x-3)-3

We multiply parentheses

-12x^2-9x-3

Back to the equation:

-(-12x^2-9x-3)


We get rid of parentheses

12x^2+9x+3-72=0

We add all the numbers together, and all the variables

12x^2+9x-69=0

a = 12; b = 9; c = -69;
Δ = b2-4ac
Δ = 92-4·12·(-69)
Δ = 3393
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:

$\sqrt{\Delta}=\sqrt{3393}=\sqrt{9*377}=\sqrt{9}*\sqrt{377}=3\sqrt{377}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{377}}{2*12}=\frac{-9-3\sqrt{377}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{377}}{2*12}=\frac{-9+3\sqrt{377}}{24}
$