1/2x-8/3x=65/24

Solution for 1/2x-8/3x=65/24 equation:

1/2x-8/3x=65/24

We move all terms to the left:

1/2x-8/3x-(65/24)=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-8/3x-(+65/24)=0

We get rid of parentheses

1/2x-8/3x-65/24=0

We calculate fractions


(-1170x^2)/288x^2+144x/288x^2+(-768x)/288x^2=0

We multiply all the terms by the denominator


(-1170x^2)+144x+(-768x)=0

We get rid of parentheses

-1170x^2+144x-768x=0

We add all the numbers together, and all the variables

-1170x^2-624x=0

a = -1170; b = -624; c = 0;
Δ = b2-4ac
Δ = -6242-4·(-1170)·0
Δ = 389376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{389376}=624$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-624)-624}{2*-1170}=\frac{0}{-2340}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-624)+624}{2*-1170}=\frac{1248}{-2340}
=-8/15
$