2/x+2=-x/x+5x+6

Solution for 2/x+2=-x/x+5x+6 equation:

2/x+2=-x/x+5x+6

We move all terms to the left:

2/x+2-(-x/x+5x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+5x+6)!=0

x∈R


We add all the numbers together, and all the variables

2/x-(5x-x/x+6)+2=0

We get rid of parentheses

2/x-5x+x/x-6+2=0

Fractions to decimals

2/x-5x-6+2+1=0

We multiply all the terms by the denominator


-5x*x-6*x+2*x+1*x+2=0

We add all the numbers together, and all the variables

-3x-5x*x+2=0

Wy multiply elements

-5x^2-3x+2=0

a = -5; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-5)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*-5}=\frac{-4}{-10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*-5}=\frac{10}{-10}
=-1
$