x+2/3x=158

Solution for x+2/3x=158 equation:

x+2/3x=158

We move all terms to the left:

x+2/3x-(158)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-158*3x+2=0

Wy multiply elements

3x^2-474x+2=0

a = 3; b = -474; c = +2;
Δ = b2-4ac
Δ = -4742-4·3·2
Δ = 224652
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:

$\sqrt{\Delta}=\sqrt{224652}=\sqrt{4*56163}=\sqrt{4}*\sqrt{56163}=2\sqrt{56163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-474)-2\sqrt{56163}}{2*3}=\frac{474-2\sqrt{56163}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-474)+2\sqrt{56163}}{2*3}=\frac{474+2\sqrt{56163}}{6}
$