2/3x+3x=35

Solution for 2/3x+3x=35 equation:

2/3x+3x=35

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-35=0

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2-105x+2=0

a = 9; b = -105; c = +2;
Δ = b2-4ac
Δ = -1052-4·9·2
Δ = 10953
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:

$\sqrt{\Delta}=\sqrt{10953}=\sqrt{9*1217}=\sqrt{9}*\sqrt{1217}=3\sqrt{1217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-3\sqrt{1217}}{2*9}=\frac{105-3\sqrt{1217}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+3\sqrt{1217}}{2*9}=\frac{105+3\sqrt{1217}}{18}
$