2(6x^2-5x)=12

Solution for 2(6x^2-5x)=12 equation:

2(6x^2-5x)=12

We move all terms to the left:

2(6x^2-5x)-(12)=0

We multiply parentheses

12x^2-10x-12=0

a = 12; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·12·(-12)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-26}{2*12}=\frac{-16}{24}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+26}{2*12}=\frac{36}{24}
=1+1/2
$