5/8x-2+1/3x=1/2

Solution for 5/8x-2+1/3x=1/2 equation:

5/8x-2+1/3x=1/2

We move all terms to the left:

5/8x-2+1/3x-(1/2)=0


Domain of the equation: 8x!=0

x!=0/8

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

5/8x+1/3x-2-(+1/2)=0

We get rid of parentheses

5/8x+1/3x-2-1/2=0

We calculate fractions


(-72x^2)/96x^2+60x/96x^2+32x/96x^2-2=0

We multiply all the terms by the denominator


(-72x^2)+60x+32x-2*96x^2=0

We add all the numbers together, and all the variables

(-72x^2)+92x-2*96x^2=0

Wy multiply elements

(-72x^2)-192x^2+92x=0

We get rid of parentheses

-72x^2-192x^2+92x=0

We add all the numbers together, and all the variables

-264x^2+92x=0

a = -264; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·(-264)·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*-264}=\frac{-184}{-528}
=23/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*-264}=\frac{0}{-528}
=0
$