3x-6=4(2-3x)8x

Solution for 3x-6=4(2-3x)8x equation:

3x-6=4(2-3x)8x

We move all terms to the left:

3x-6-(4(2-3x)8x)=0

We add all the numbers together, and all the variables

3x-(4(-3x+2)8x)-6=0


We calculate terms in parentheses: -(4(-3x+2)8x), so:

4(-3x+2)8x

We multiply parentheses

-96x^2+64x

Back to the equation:

-(-96x^2+64x)


We get rid of parentheses

96x^2-64x+3x-6=0

We add all the numbers together, and all the variables

96x^2-61x-6=0

a = 96; b = -61; c = -6;
Δ = b2-4ac
Δ = -612-4·96·(-6)
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-5\sqrt{241}}{2*96}=\frac{61-5\sqrt{241}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+5\sqrt{241}}{2*96}=\frac{61+5\sqrt{241}}{192}
$