x(3x-4)=39

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

x(3x-4)=39

We move all terms to the left:

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

We multiply parentheses

3x^2-4x-39=0

a = 3; b = -4; c = -39;
Δ = b2-4ac
Δ = -42-4·3·(-39)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-22}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+22}{2*3}=\frac{26}{6}
=4+1/3
$