2x-6/x+2=7

Solution for 2x-6/x+2=7 equation:

2x-6/x+2=7

We move all terms to the left:

2x-6/x+2-(7)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-6/x-5=0

We multiply all the terms by the denominator


2x*x-5*x-6=0

We add all the numbers together, and all the variables

-5x+2x*x-6=0

Wy multiply elements

2x^2-5x-6=0

a = 2; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·2·(-6)
Δ = 73
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{-(-5)-\sqrt{73}}{2*2}=\frac{5-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*2}=\frac{5+\sqrt{73}}{4}
$