(2x-2)x=35

Solution for (2x-2)x=35 equation:

(2x-2)x=35

We move all terms to the left:

(2x-2)x-(35)=0

We multiply parentheses

2x^2-2x-35=0

a = 2; b = -2; c = -35;
Δ = b2-4ac
Δ = -22-4·2·(-35)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{71}}{2*2}=\frac{2-2\sqrt{71}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{71}}{2*2}=\frac{2+2\sqrt{71}}{4}
$