-200=(x-30)(30-x)

Solution for -200=(x-30)(30-x) equation:

-200=(x-30)(30-x)

We move all terms to the left:

-200-((x-30)(30-x))=0

We add all the numbers together, and all the variables

-((x-30)(-1x+30))-200=0

We multiply parentheses ..

-((-1x^2+30x+30x-900))-200=0


We calculate terms in parentheses: -((-1x^2+30x+30x-900)), so:

(-1x^2+30x+30x-900)

We get rid of parentheses

-1x^2+30x+30x-900

We add all the numbers together, and all the variables

-1x^2+60x-900

Back to the equation:

-(-1x^2+60x-900)


We get rid of parentheses

1x^2-60x+900-200=0

We add all the numbers together, and all the variables

x^2-60x+700=0

a = 1; b = -60; c = +700;
Δ = b2-4ac
Δ = -602-4·1·700
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{2}}{2*1}=\frac{60-20\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{2}}{2*1}=\frac{60+20\sqrt{2}}{2}
$