x/5=x^2/x+2

Solution for x/5=x^2/x+2 equation:

x/5=x^2/x+2

We move all terms to the left:

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


Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

x^2+(-5x^2)-10x=0

We get rid of parentheses

x^2-5x^2-10x=0

We add all the numbers together, and all the variables

-4x^2-10x=0

a = -4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-4}=\frac{20}{-8}
=-2+1/2
$