2x/x-2=7+19x^2/x-2

Solution for 2x/x-2=7+19x^2/x-2 equation:

2x/x-2=7+19x^2/x-2

We move all terms to the left:

2x/x-2-(7+19x^2/x-2)=0


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

x∈R



Domain of the equation: x!=0

x∈R


We get rid of parentheses

-19x^2/x+2x/x-7+2-2=0

We multiply all the terms by the denominator


-19x^2+2x-7*x+2*x-2*x=0

We add all the numbers together, and all the variables

-19x^2-5x=0

a = -19; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-19)·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*-19}=\frac{0}{-38}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-19}=\frac{10}{-38}
=-5/19
$