2x(-3+4x)=39

Solution for 2x(-3+4x)=39 equation:

2x(-3+4x)=39

We move all terms to the left:

2x(-3+4x)-(39)=0

We add all the numbers together, and all the variables

2x(4x-3)-39=0

We multiply parentheses

8x^2-6x-39=0

a = 8; b = -6; c = -39;
Δ = b2-4ac
Δ = -62-4·8·(-39)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{321}}{2*8}=\frac{6-2\sqrt{321}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{321}}{2*8}=\frac{6+2\sqrt{321}}{16}
$