200/10-27/x=1.1x

Solution for 200/10-27/x=1.1x equation:

200/10-27/x=1.1x

We move all terms to the left:

200/10-27/x-(1.1x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-27/x-(+1.1x)+200/10=0

We add all the numbers together, and all the variables

-27/x-(+1.1x)+20=0

We get rid of parentheses

-27/x-1.1x+20=0

We multiply all the terms by the denominator


-(1.1x)*x+20*x-27=0

We add all the numbers together, and all the variables

-(+1.1x)*x+20*x-27=0

We add all the numbers together, and all the variables

20x-(+1.1x)*x-27=0

We multiply parentheses

-x^2+20x-27=0

We add all the numbers together, and all the variables

-1x^2+20x-27=0

a = -1; b = 20; c = -27;
Δ = b2-4ac
Δ = 202-4·(-1)·(-27)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{73}}{2*-1}=\frac{-20-2\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{73}}{2*-1}=\frac{-20+2\sqrt{73}}{-2}
$