1/2x-10/3+5/8x=-31/12

Solution for 1/2x-10/3+5/8x=-31/12 equation:

1/2x-10/3+5/8x=-31/12

We move all terms to the left:

1/2x-10/3+5/8x-(-31/12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/2x+5/8x-10/3+31/12=0

We calculate fractions


(-15360x^2)/1728x^2+11904x^2/1728x^2+864x/1728x^2+1080x/1728x^2=0

We multiply all the terms by the denominator


(-15360x^2)+11904x^2+864x+1080x=0

We add all the numbers together, and all the variables

11904x^2+(-15360x^2)+1944x=0

We get rid of parentheses

11904x^2-15360x^2+1944x=0

We add all the numbers together, and all the variables

-3456x^2+1944x=0

a = -3456; b = 1944; c = 0;
Δ = b2-4ac
Δ = 19442-4·(-3456)·0
Δ = 3779136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3779136}=1944$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1944)-1944}{2*-3456}=\frac{-3888}{-6912}
=9/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1944)+1944}{2*-3456}=\frac{0}{-6912}
=0
$