x+4/3x=48

Solution for x+4/3x=48 equation:

x+4/3x=48

We move all terms to the left:

x+4/3x-(48)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-48*3x+4=0

Wy multiply elements

3x^2-144x+4=0

a = 3; b = -144; c = +4;
Δ = b2-4ac
Δ = -1442-4·3·4
Δ = 20688
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:

$\sqrt{\Delta}=\sqrt{20688}=\sqrt{16*1293}=\sqrt{16}*\sqrt{1293}=4\sqrt{1293}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1293}}{2*3}=\frac{144-4\sqrt{1293}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1293}}{2*3}=\frac{144+4\sqrt{1293}}{6}
$