(5x+7)/x-1=3x+2

Solution for (5x+7)/x-1=3x+2 equation:

(5x+7)/x-1=3x+2

We move all terms to the left:

(5x+7)/x-1-(3x+2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

(5x+7)/x-3x-2-1=0

We multiply all the terms by the denominator


(5x+7)-3x*x-2*x-1*x=0

We add all the numbers together, and all the variables

-3x+(5x+7)-3x*x=0

Wy multiply elements

-3x^2-3x+(5x+7)=0

We get rid of parentheses

-3x^2-3x+5x+7=0

We add all the numbers together, and all the variables

-3x^2+2x+7=0

a = -3; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-3)·7
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*-3}=\frac{-2-2\sqrt{22}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*-3}=\frac{-2+2\sqrt{22}}{-6}
$