8x(-3x-2)=4(3x-1)

Solution for 8x(-3x-2)=4(3x-1) equation:

8x(-3x-2)=4(3x-1)

We move all terms to the left:

8x(-3x-2)-(4(3x-1))=0

We multiply parentheses

-24x^2-16x-(4(3x-1))=0


We calculate terms in parentheses: -(4(3x-1)), so:

4(3x-1)

We multiply parentheses

12x-4

Back to the equation:

-(12x-4)


We get rid of parentheses

-24x^2-16x-12x+4=0

We add all the numbers together, and all the variables

-24x^2-28x+4=0

a = -24; b = -28; c = +4;
Δ = b2-4ac
Δ = -282-4·(-24)·4
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{73}}{2*-24}=\frac{28-4\sqrt{73}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{73}}{2*-24}=\frac{28+4\sqrt{73}}{-48}
$