2/3x+x-4=31

Solution for 2/3x+x-4=31 equation:

2/3x+x-4=31

We move all terms to the left:

2/3x+x-4-(31)=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-35=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-105x+2=0

a = 3; b = -105; c = +2;
Δ = b2-4ac
Δ = -1052-4·3·2
Δ = 11001
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{11001}}{2*3}=\frac{105-\sqrt{11001}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11001}}{2*3}=\frac{105+\sqrt{11001}}{6}
$