12+3x=3-1/2x

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

12+3x=3-1/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x+1/2x-3+12=0

We multiply all the terms by the denominator


3x*2x-3*2x+12*2x+1=0

Wy multiply elements

6x^2-6x+24x+1=0

We add all the numbers together, and all the variables

6x^2+18x+1=0

a = 6; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·6·1
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{3}}{2*6}=\frac{-18-10\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{3}}{2*6}=\frac{-18+10\sqrt{3}}{12}
$