2x(3x-2)=78

Solution for 2x(3x-2)=78 equation:

2x(3x-2)=78

We move all terms to the left:

2x(3x-2)-(78)=0

We multiply parentheses

6x^2-4x-78=0

a = 6; b = -4; c = -78;
Δ = b2-4ac
Δ = -42-4·6·(-78)
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{118}}{2*6}=\frac{4-4\sqrt{118}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{118}}{2*6}=\frac{4+4\sqrt{118}}{12}
$