x/x+4=2x-6/x+12

Solution for x/x+4=2x-6/x+12 equation:

x/x+4=2x-6/x+12

We move all terms to the left:

x/x+4-(2x-6/x+12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+12)!=0

x∈R


We get rid of parentheses

x/x-2x+6/x-12+4=0

Fractions to decimals

6/x-2x-12+4+1=0

We multiply all the terms by the denominator


-2x*x-12*x+4*x+1*x+6=0

We add all the numbers together, and all the variables

-7x-2x*x+6=0

Wy multiply elements

-2x^2-7x+6=0

a = -2; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·(-2)·6
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*-2}=\frac{7-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*-2}=\frac{7+\sqrt{97}}{-4}
$