3(x-6)=-1/2x

Solution for 3(x-6)=-1/2x equation:

3(x-6)=-1/2x

We move all terms to the left:

3(x-6)-(-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

3x-(-1/2x)-18=0

We get rid of parentheses

3x+1/2x-18=0

We multiply all the terms by the denominator


3x*2x-18*2x+1=0

Wy multiply elements

6x^2-36x+1=0

a = 6; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·6·1
Δ = 1272
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:

$\sqrt{\Delta}=\sqrt{1272}=\sqrt{4*318}=\sqrt{4}*\sqrt{318}=2\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{318}}{2*6}=\frac{36-2\sqrt{318}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{318}}{2*6}=\frac{36+2\sqrt{318}}{12}
$