12x-24+3x=1/2x=3+2

Solution for 12x-24+3x=1/2x=3+2 equation:

12x-24+3x=1/2x=3+2

We move all terms to the left:

12x-24+3x-(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

12x+3x-(+1/2x)-24=0

We add all the numbers together, and all the variables

15x-(+1/2x)-24=0

We get rid of parentheses

15x-1/2x-24=0

We multiply all the terms by the denominator


15x*2x-24*2x-1=0

Wy multiply elements

30x^2-48x-1=0

a = 30; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·30·(-1)
Δ = 2424
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:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{606}}{2*30}=\frac{48-2\sqrt{606}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{606}}{2*30}=\frac{48+2\sqrt{606}}{60}
$