90-x-x^2/x^2-12x+27*6x/x+10=x

Solution for 90-x-x^2/x^2-12x+27*6x/x+10=x equation:

90-x-x^2/x^2-12x+27*6x/x+10=x

We move all terms to the left:

90-x-x^2/x^2-12x+27*6x/x+10-(x)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-x^2/x^2-14x+27*6x/x+100=0

Fractions to decimals

27*6x/x-14x+100+1=0

We multiply all the terms by the denominator


27*6x-14x*x+100*x+1*x=0

We add all the numbers together, and all the variables

101x+27*6x-14x*x=0

Wy multiply elements

-14x^2+101x+162x=0

We add all the numbers together, and all the variables

-14x^2+263x=0

a = -14; b = 263; c = 0;
Δ = b2-4ac
Δ = 2632-4·(-14)·0
Δ = 69169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{69169}=263$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(263)-263}{2*-14}=\frac{-526}{-28}
=18+11/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(263)+263}{2*-14}=\frac{0}{-28}
=0
$