5x-6/x+3=2

Solution for 5x-6/x+3=2 equation:

5x-6/x+3=2

We move all terms to the left:

5x-6/x+3-(2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-6/x+1=0

We multiply all the terms by the denominator


5x*x+1*x-6=0

We add all the numbers together, and all the variables

x+5x*x-6=0

Wy multiply elements

5x^2+x-6=0

a = 5; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·5·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*5}=\frac{-12}{10}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*5}=\frac{10}{10}
=1
$