x+4x/x-3=12/x-3

Solution for x+4x/x-3=12/x-3 equation:

x+4x/x-3=12/x-3

We move all terms to the left:

x+4x/x-3-(12/x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

x+4x/x-12/x+3-3=0

We multiply all the terms by the denominator


x*x+4x+3*x-3*x-12=0

We add all the numbers together, and all the variables

4x+x*x-12=0

Wy multiply elements

x^2+4x-12=0

a = 1; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*1}=\frac{4}{2}
=2
$