57=(1/2)(201+1-11x)

Solution for 57=(1/2)(201+1-11x) equation:

57=(1/2)(201+1-11x)

We move all terms to the left:

57-((1/2)(201+1-11x))=0


Domain of the equation: 2)(201+1-11x))!=0

We move all terms containing x to the left, all other terms to the right

-11x))+2)(201!=-1

x∈R


We add all the numbers together, and all the variables

-((+1/2)(-11x+202))+57=0

We multiply parentheses ..

-((-11x^2+1/2*202))+57=0

We multiply all the terms by the denominator


-((-11x^2+1+57*2*202))=0


We calculate terms in parentheses: -((-11x^2+1+57*2*202)), so:

(-11x^2+1+57*2*202)

We get rid of parentheses

-11x^2+1+57*2*202

We add all the numbers together, and all the variables

-11x^2+23029

Back to the equation:

-(-11x^2+23029)


We get rid of parentheses

11x^2-23029=0

a = 11; b = 0; c = -23029;
Δ = b2-4ac
Δ = 02-4·11·(-23029)
Δ = 1013276
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:

$\sqrt{\Delta}=\sqrt{1013276}=\sqrt{4*253319}=\sqrt{4}*\sqrt{253319}=2\sqrt{253319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{253319}}{2*11}=\frac{0-2\sqrt{253319}}{22}
=-\frac{2\sqrt{253319}}{22}
=-\frac{\sqrt{253319}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{253319}}{2*11}=\frac{0+2\sqrt{253319}}{22}
=\frac{2\sqrt{253319}}{22}
=\frac{\sqrt{253319}}{11}
$