1400=2x^2-200x

Solution for 1400=2x^2-200x equation:

1400=2x^2-200x

We move all terms to the left:

1400-(2x^2-200x)=0

We get rid of parentheses

-2x^2+200x+1400=0

a = -2; b = 200; c = +1400;
Δ = b2-4ac
Δ = 2002-4·(-2)·1400
Δ = 51200
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:

$\sqrt{\Delta}=\sqrt{51200}=\sqrt{25600*2}=\sqrt{25600}*\sqrt{2}=160\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-160\sqrt{2}}{2*-2}=\frac{-200-160\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+160\sqrt{2}}{2*-2}=\frac{-200+160\sqrt{2}}{-4}
$