X^2=(11-x)*100

Solution for X^2=(11-x)*100 equation:

X^2=(11-X)*100

We move all terms to the left:

X^2-((11-X)*100)=0

We add all the numbers together, and all the variables

X^2-((-1X+11)*100)=0


We calculate terms in parentheses: -((-1X+11)*100), so:

(-1X+11)*100

We multiply parentheses

-100X+1100

Back to the equation:

-(-100X+1100)


We get rid of parentheses

X^2+100X-1100=0

a = 1; b = 100; c = -1100;
Δ = b2-4ac
Δ = 1002-4·1·(-1100)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-120}{2*1}=\frac{-220}{2}
=-110
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+120}{2*1}=\frac{20}{2}
=10
$