2/5x+4/15x=10

Solution for 2/5x+4/15x=10 equation:

2/5x+4/15x=10

We move all terms to the left:

2/5x+4/15x-(10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R


We calculate fractions


30x/75x^2+20x/75x^2-10=0

We multiply all the terms by the denominator


30x+20x-10*75x^2=0

We add all the numbers together, and all the variables

50x-10*75x^2=0

Wy multiply elements

-750x^2+50x=0

a = -750; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-750)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-750}=\frac{-100}{-1500}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-750}=\frac{0}{-1500}
=0
$