2x+3/x-1=-7x+10/x-1

Solution for 2x+3/x-1=-7x+10/x-1 equation:

2x+3/x-1=-7x+10/x-1

We move all terms to the left:

2x+3/x-1-(-7x+10/x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

2x+3/x+7x-10/x+1-1=0

We multiply all the terms by the denominator


2x*x+7x*x+1*x-1*x+3-10=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

9x^2-7=0

a = 9; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·9·(-7)
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*9}=\frac{0-6\sqrt{7}}{18}
=-\frac{6\sqrt{7}}{18}
=-\frac{\sqrt{7}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*9}=\frac{0+6\sqrt{7}}{18}
=\frac{6\sqrt{7}}{18}
=\frac{\sqrt{7}}{3}
$