-7/8x+13/3x=-83/24

Solution for -7/8x+13/3x=-83/24 equation:

-7/8x+13/3x=-83/24

We move all terms to the left:

-7/8x+13/3x-(-83/24)=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 get rid of parentheses

-7/8x+13/3x+83/24=0

We calculate fractions


5976x^2/1152x^2+(-1008x)/1152x^2+4992x/1152x^2=0

We multiply all the terms by the denominator


5976x^2+(-1008x)+4992x=0

We add all the numbers together, and all the variables

5976x^2+4992x+(-1008x)=0

We get rid of parentheses

5976x^2+4992x-1008x=0

We add all the numbers together, and all the variables

5976x^2+3984x=0

a = 5976; b = 3984; c = 0;
Δ = b2-4ac
Δ = 39842-4·5976·0
Δ = 15872256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15872256}=3984$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3984)-3984}{2*5976}=\frac{-7968}{11952}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3984)+3984}{2*5976}=\frac{0}{11952}
=0
$