2(3X2-5)-4(x-1)=2

Solution for 2(3X2-5)-4(x-1)=2 equation:

2(3X^2-5)-4(X-1)=2

We move all terms to the left:

2(3X^2-5)-4(X-1)-(2)=0

We multiply parentheses

6X^2-4X-10+4-2=0

We add all the numbers together, and all the variables

6X^2-4X-8=0

a = 6; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·6·(-8)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{13}}{2*6}=\frac{4-4\sqrt{13}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{13}}{2*6}=\frac{4+4\sqrt{13}}{12}
$