x=(5x+5x^2)/X

Solution for x=(5x+5x^2)/X equation:

x=(5x+5x^2)/x

We move all terms to the left:

x-((5x+5x^2)/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-((5x+5x^2)+x*x)=0


We calculate terms in parentheses: -((5x+5x^2)+x*x), so:

(5x+5x^2)+x*x

Wy multiply elements

(5x+5x^2)+x^2

We get rid of parentheses

5x^2+x^2+5x

We add all the numbers together, and all the variables

6x^2+5x

Back to the equation:

-(6x^2+5x)


We get rid of parentheses

-6x^2-5x=0

a = -6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-6)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-6}=\frac{10}{-12}
=-5/6
$