2x-3/x-3-2=12/x+3

Solution for 2x-3/x-3-2=12/x+3 equation:

2x-3/x-3-2=12/x+3

We move all terms to the left:

2x-3/x-3-2-(12/x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We add all the numbers together, and all the variables

2x-3/x-(12/x+3)-5=0

We get rid of parentheses

2x-3/x-12/x-3-5=0

We multiply all the terms by the denominator


2x*x-3*x-5*x-3-12=0

We add all the numbers together, and all the variables

-8x+2x*x-15=0

Wy multiply elements

2x^2-8x-15=0

a = 2; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·2·(-15)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{46}}{2*2}=\frac{8-2\sqrt{46}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{46}}{2*2}=\frac{8+2\sqrt{46}}{4}
$