8/5x+1/10x=50/15

Solution for 8/5x+1/10x=50/15 equation:

8/5x+1/10x=50/15

We move all terms to the left:

8/5x+1/10x-(50/15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

8/5x+1/10x-(+50/15)=0

We get rid of parentheses

8/5x+1/10x-50/15=0

We calculate fractions


(-2500x^2)/750x^2+1200x/750x^2+75x/750x^2=0

We multiply all the terms by the denominator


(-2500x^2)+1200x+75x=0

We add all the numbers together, and all the variables

(-2500x^2)+1275x=0

We get rid of parentheses

-2500x^2+1275x=0

a = -2500; b = 1275; c = 0;
Δ = b2-4ac
Δ = 12752-4·(-2500)·0
Δ = 1625625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1625625}=1275$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1275)-1275}{2*-2500}=\frac{-2550}{-5000}
=51/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1275)+1275}{2*-2500}=\frac{0}{-5000}
=0
$