1200=2x^2-2x

Solution for 1200=2x^2-2x equation:

1200=2x^2-2x

We move all terms to the left:

1200-(2x^2-2x)=0

We get rid of parentheses

-2x^2+2x+1200=0

a = -2; b = 2; c = +1200;
Δ = b2-4ac
Δ = 22-4·(-2)·1200
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-98}{2*-2}=\frac{-100}{-4}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+98}{2*-2}=\frac{96}{-4}
=-24
$