4=4/3*x

Solution for 4=4/3*x equation:

4=4/3*x

We move all terms to the left:

4-(4/3*x)=0


Domain of the equation: 3*x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+4/3*x)+4=0

We get rid of parentheses

-4/3*x+4=0

We multiply all the terms by the denominator


4*3*x-4=0

Wy multiply elements

12x*x-4=0

Wy multiply elements

12x^2-4=0

a = 12; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·12·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*12}=\frac{0-8\sqrt{3}}{24}
=-\frac{8\sqrt{3}}{24}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*12}=\frac{0+8\sqrt{3}}{24}
=\frac{8\sqrt{3}}{24}
=\frac{\sqrt{3}}{3}
$