3x+12-x=61/2x+1+x+1

Solution for 3x+12-x=61/2x+1+x+1 equation:

3x+12-x=61/2x+1+x+1

We move all terms to the left:

3x+12-x-(61/2x+1+x+1)=0


Domain of the equation: 2x+1+x+1)!=0

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

2x+x+1)!=-1

x∈R


We add all the numbers together, and all the variables

3x-x-(x+61/2x+2)+12=0

We add all the numbers together, and all the variables

2x-(x+61/2x+2)+12=0

We get rid of parentheses

2x-x-61/2x-2+12=0

We multiply all the terms by the denominator


2x*2x-x*2x-2*2x+12*2x-61=0

Wy multiply elements

4x^2-2x^2-4x+24x-61=0

We add all the numbers together, and all the variables

2x^2+20x-61=0

a = 2; b = 20; c = -61;
Δ = b2-4ac
Δ = 202-4·2·(-61)
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{222}}{2*2}=\frac{-20-2\sqrt{222}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{222}}{2*2}=\frac{-20+2\sqrt{222}}{4}
$