.5x+4=2/3x

Solution for .5x+4=2/3x equation:

.5x+4=2/3x

We move all terms to the left:

.5x+4-(2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.5x-(+2/3x)+4=0

We get rid of parentheses

.5x-2/3x+4=0

We multiply all the terms by the denominator


(.5x)*3x+4*3x-2=0

We add all the numbers together, and all the variables

(+.5x)*3x+4*3x-2=0

We multiply parentheses

3x^2+4*3x-2=0

Wy multiply elements

3x^2+12x-2=0

a = 3; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·3·(-2)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*3}=\frac{-12-2\sqrt{42}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*3}=\frac{-12+2\sqrt{42}}{6}
$