2x(4x+3)=39

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

2x(4x+3)=39

We move all terms to the left:

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}
$