1/2x+2=3x

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

1/2x+2=3x

We move all terms to the left:

1/2x+2-(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

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-6)·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*-6}=\frac{-4-2\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*-6}=\frac{-4+2\sqrt{10}}{-12}
$