2/5x-5/8x=5/12

Solution for 2/5x-5/8x=5/12 equation:

2/5x-5/8x=5/12

We move all terms to the left:

2/5x-5/8x-(5/12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-5/8x-(+5/12)=0

We get rid of parentheses

2/5x-5/8x-5/12=0

We calculate fractions


(-1600x^2)/480x^2+192x/480x^2+(-300x)/480x^2=0

We multiply all the terms by the denominator


(-1600x^2)+192x+(-300x)=0

We get rid of parentheses

-1600x^2+192x-300x=0

We add all the numbers together, and all the variables

-1600x^2-108x=0

a = -1600; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·(-1600)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*-1600}=\frac{0}{-3200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*-1600}=\frac{216}{-3200}
=-27/400
$