2(x^2-x)=138

Solution for 2(x^2-x)=138 equation:

2(x^2-x)=138

We move all terms to the left:

2(x^2-x)-(138)=0

We multiply parentheses

2x^2-2x-138=0

a = 2; b = -2; c = -138;
Δ = b2-4ac
Δ = -22-4·2·(-138)
Δ = 1108
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:

$\sqrt{\Delta}=\sqrt{1108}=\sqrt{4*277}=\sqrt{4}*\sqrt{277}=2\sqrt{277}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{277}}{2*2}=\frac{2-2\sqrt{277}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{277}}{2*2}=\frac{2+2\sqrt{277}}{4}
$