2/3x+x=115

Solution for 2/3x+x=115 equation:

2/3x+x=115

We move all terms to the left:

2/3x+x-(115)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/3x-115=0

We multiply all the terms by the denominator


x*3x-115*3x+2=0

Wy multiply elements

3x^2-345x+2=0

a = 3; b = -345; c = +2;
Δ = b2-4ac
Δ = -3452-4·3·2
Δ = 119001
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{-(-345)-\sqrt{119001}}{2*3}=\frac{345-\sqrt{119001}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-345)+\sqrt{119001}}{2*3}=\frac{345+\sqrt{119001}}{6}
$