4/3x+x=28

Solution for 4/3x+x=28 equation:

4/3x+x=28

We move all terms to the left:

4/3x+x-(28)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/3x-28=0

We multiply all the terms by the denominator


x*3x-28*3x+4=0

Wy multiply elements

3x^2-84x+4=0

a = 3; b = -84; c = +4;
Δ = b2-4ac
Δ = -842-4·3·4
Δ = 7008
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:

$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{438}}{2*3}=\frac{84-4\sqrt{438}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{438}}{2*3}=\frac{84+4\sqrt{438}}{6}
$