x+1/3x=51

Solution for x+1/3x=51 equation:

x+1/3x=51

We move all terms to the left:

x+1/3x-(51)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-51*3x+1=0

Wy multiply elements

3x^2-153x+1=0

a = 3; b = -153; c = +1;
Δ = b2-4ac
Δ = -1532-4·3·1
Δ = 23397
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-153)-\sqrt{23397}}{2*3}=\frac{153-\sqrt{23397}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-153)+\sqrt{23397}}{2*3}=\frac{153+\sqrt{23397}}{6}
$