3(4x-2)=8x(4x-9)

Solution for 3(4x-2)=8x(4x-9) equation:

3(4x-2)=8x(4x-9)

We move all terms to the left:

3(4x-2)-(8x(4x-9))=0

We multiply parentheses

12x-(8x(4x-9))-6=0


We calculate terms in parentheses: -(8x(4x-9)), so:

8x(4x-9)

We multiply parentheses

32x^2-72x

Back to the equation:

-(32x^2-72x)


We get rid of parentheses

-32x^2+12x+72x-6=0

We add all the numbers together, and all the variables

-32x^2+84x-6=0

a = -32; b = 84; c = -6;
Δ = b2-4ac
Δ = 842-4·(-32)·(-6)
Δ = 6288
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:

$\sqrt{\Delta}=\sqrt{6288}=\sqrt{16*393}=\sqrt{16}*\sqrt{393}=4\sqrt{393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{393}}{2*-32}=\frac{-84-4\sqrt{393}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{393}}{2*-32}=\frac{-84+4\sqrt{393}}{-64}
$