3x-12/x-4=2x-5

Solution for 3x-12/x-4=2x-5 equation:

3x-12/x-4=2x-5

We move all terms to the left:

3x-12/x-4-(2x-5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3x-12/x-2x+5-4=0

We multiply all the terms by the denominator


3x*x-2x*x+5*x-4*x-12=0

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-2x^2+x-12=0

We add all the numbers together, and all the variables

x^2+x-12=0

a = 1; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*1}=\frac{6}{2}
=3
$