12x-(42-3x)/(x+1)=42

Solution for 12x-(42-3x)/(x+1)=42 equation:

12x-(42-3x)/(x+1)=42

We move all terms to the left:

12x-(42-3x)/(x+1)-(42)=0


Domain of the equation: (x+1)!=0

We move all terms containing x to the left, all other terms to the right

x!=-1

x∈R


We add all the numbers together, and all the variables

12x-(-3x+42)/(x+1)-42=0

We multiply all the terms by the denominator


12x*(x+1)-(-3x+42)-42*(x+1)=0

We multiply parentheses

12x^2+12x-(-3x+42)-42x-42=0

We get rid of parentheses

12x^2+12x+3x-42x-42-42=0

We add all the numbers together, and all the variables

12x^2-27x-84=0

a = 12; b = -27; c = -84;
Δ = b2-4ac
Δ = -272-4·12·(-84)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-69}{2*12}=\frac{-42}{24}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+69}{2*12}=\frac{96}{24}
=4
$