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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+24-2x)!=0

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

2x-2x)!=-24

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


3x*2x+2x*2x-24*2x-12*2x-1=0

Wy multiply elements

6x^2+4x^2-48x-24x-1=0

We add all the numbers together, and all the variables

10x^2-72x-1=0

a = 10; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·10·(-1)
Δ = 5224
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:

$\sqrt{\Delta}=\sqrt{5224}=\sqrt{4*1306}=\sqrt{4}*\sqrt{1306}=2\sqrt{1306}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1306}}{2*10}=\frac{72-2\sqrt{1306}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1306}}{2*10}=\frac{72+2\sqrt{1306}}{20}
$