-5/8x-7/24+1/3x=-56

Solution for -5/8x-7/24+1/3x=-56 equation:

-5/8x-7/24+1/3x=-56

We move all terms to the left:

-5/8x-7/24+1/3x-(-56)=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+56-7/24=0

We calculate fractions


(-504x^2)/1152x^2+(-720x)/1152x^2+384x/1152x^2+56=0

We multiply all the terms by the denominator


(-504x^2)+(-720x)+384x+56*1152x^2=0

We add all the numbers together, and all the variables

(-504x^2)+384x+(-720x)+56*1152x^2=0

Wy multiply elements

(-504x^2)+64512x^2+384x+(-720x)=0

We get rid of parentheses

-504x^2+64512x^2+384x-720x=0

We add all the numbers together, and all the variables

64008x^2-336x=0

a = 64008; b = -336; c = 0;
Δ = b2-4ac
Δ = -3362-4·64008·0
Δ = 112896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{112896}=336$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-336}{2*64008}=\frac{0}{128016}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+336}{2*64008}=\frac{672}{128016}
=2/381
$