210=(10-27/x)*1.1x

Solution for 210=(10-27/x)*1.1x equation:

210=(10-27/x)*1.1x

We move all terms to the left:

210-((10-27/x)*1.1x)=0


Domain of the equation: x)*1.1x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-((-27/x+10)*1.1x)+210=0

We multiply all the terms by the denominator


-((-27+210*x+10)*1.1x)=0


We calculate terms in parentheses: -((-27+210*x+10)*1.1x), so:

(-27+210*x+10)*1.1x

We add all the numbers together, and all the variables

(210x-17)*1.1x

We multiply parentheses

210x^2-17x

Back to the equation:

-(210x^2-17x)


We get rid of parentheses

-210x^2+17x=0

a = -210; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-210)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-210}=\frac{-34}{-420}
=17/210
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-210}=\frac{0}{-420}
=0
$