5-1/2x=12+3x

Solution for 5-1/2x=12+3x equation:

5-1/2x=12+3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-3x*2x-12*2x+5*2x-1=0

Wy multiply elements

-6x^2-24x+10x-1=0

We add all the numbers together, and all the variables

-6x^2-14x-1=0

a = -6; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-6)·(-1)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{43}}{2*-6}=\frac{14-2\sqrt{43}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{43}}{2*-6}=\frac{14+2\sqrt{43}}{-12}
$