6x(5x-1)=2

Solution for 6x(5x-1)=2 equation:

6x(5x-1)=2

We move all terms to the left:

6x(5x-1)-(2)=0

We multiply parentheses

30x^2-6x-2=0

a = 30; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·30·(-2)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*30}=\frac{6-2\sqrt{69}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*30}=\frac{6+2\sqrt{69}}{60}
$