x+1/3x=148

Solution for x+1/3x=148 equation:

x+1/3x=148

We move all terms to the left:

x+1/3x-(148)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-148*3x+1=0

Wy multiply elements

3x^2-444x+1=0

a = 3; b = -444; c = +1;
Δ = b2-4ac
Δ = -4442-4·3·1
Δ = 197124
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:

$\sqrt{\Delta}=\sqrt{197124}=\sqrt{4*49281}=\sqrt{4}*\sqrt{49281}=2\sqrt{49281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-444)-2\sqrt{49281}}{2*3}=\frac{444-2\sqrt{49281}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-444)+2\sqrt{49281}}{2*3}=\frac{444+2\sqrt{49281}}{6}
$