3/8x+5/15x=15/2

Solution for 3/8x+5/15x=15/2 equation:

3/8x+5/15x=15/2

We move all terms to the left:

3/8x+5/15x-(15/2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x+5/15x-(+15/2)=0

We get rid of parentheses

3/8x+5/15x-15/2=0

We calculate fractions


(-1800x^2)/480x^2+180x/480x^2+160x/480x^2=0

We multiply all the terms by the denominator


(-1800x^2)+180x+160x=0

We add all the numbers together, and all the variables

(-1800x^2)+340x=0

We get rid of parentheses

-1800x^2+340x=0

a = -1800; b = 340; c = 0;
Δ = b2-4ac
Δ = 3402-4·(-1800)·0
Δ = 115600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{115600}=340$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(340)-340}{2*-1800}=\frac{-680}{-3600}
=17/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(340)+340}{2*-1800}=\frac{0}{-3600}
=0
$