x^2/x^2-6=3-2x/x^2-6

Solution for x^2/x^2-6=3-2x/x^2-6 equation:

x^2/x^2-6=3-2x/x^2-6

We move all terms to the left:

x^2/x^2-6-(3-2x/x^2-6)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R



Domain of the equation: x^2-6)!=0

x∈R


We get rid of parentheses

x^2/x^2+2x/x^2-3+6-6=0

Fractions to decimals

2x/x^2-3+6-6+1=0

We multiply all the terms by the denominator


2x-3*x^2+6*x^2-6*x^2+1*x^2=0

We add all the numbers together, and all the variables

-2x^2+2x=0

a = -2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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