2x-1/3x=35

Solution for 2x-1/3x=35 equation:

2x-1/3x=35

We move all terms to the left:

2x-1/3x-(35)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-35*3x-1=0

Wy multiply elements

6x^2-105x-1=0

a = 6; b = -105; c = -1;
Δ = b2-4ac
Δ = -1052-4·6·(-1)
Δ = 11049
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{-(-105)-\sqrt{11049}}{2*6}=\frac{105-\sqrt{11049}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11049}}{2*6}=\frac{105+\sqrt{11049}}{12}
$