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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+3+2)!=0

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

2x+2)!=-3

x∈R


We add all the numbers together, and all the variables

12x+3x-(1/2x+5)-2=0

We add all the numbers together, and all the variables

15x-(1/2x+5)-2=0

We get rid of parentheses

15x-1/2x-5-2=0

We multiply all the terms by the denominator


15x*2x-5*2x-2*2x-1=0

Wy multiply elements

30x^2-10x-4x-1=0

We add all the numbers together, and all the variables

30x^2-14x-1=0

a = 30; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·30·(-1)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{79}}{2*30}=\frac{14-2\sqrt{79}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{79}}{2*30}=\frac{14+2\sqrt{79}}{60}
$