1/2x+2/3x+5=1/3

Solution for 1/2x+2/3x+5=1/3 equation:

1/2x+2/3x+5=1/3

We move all terms to the left:

1/2x+2/3x+5-(1/3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+2/3x+5-(+1/3)=0

We get rid of parentheses

1/2x+2/3x+5-1/3=0

We calculate fractions


27x/54x^2+4x/54x^2+(-2x)/54x^2+5=0

We multiply all the terms by the denominator


27x+4x+(-2x)+5*54x^2=0

We add all the numbers together, and all the variables

31x+(-2x)+5*54x^2=0

Wy multiply elements

270x^2+31x+(-2x)=0

We get rid of parentheses

270x^2+31x-2x=0

We add all the numbers together, and all the variables

270x^2+29x=0

a = 270; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·270·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*270}=\frac{-58}{540}
=-29/270
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*270}=\frac{0}{540}
=0
$