4/3x=14-x

Solution for 4/3x=14-x equation:

4/3x=14-x

We move all terms to the left:

4/3x-(14-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-1x+14)=0

We get rid of parentheses

4/3x+1x-14=0

We multiply all the terms by the denominator


1x*3x-14*3x+4=0

Wy multiply elements

3x^2-42x+4=0

a = 3; b = -42; c = +4;
Δ = b2-4ac
Δ = -422-4·3·4
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{429}}{2*3}=\frac{42-2\sqrt{429}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{429}}{2*3}=\frac{42+2\sqrt{429}}{6}
$