2/5x+1/2x=15

Solution for 2/5x+1/2x=15 equation:

2/5x+1/2x=15

We move all terms to the left:

2/5x+1/2x-(15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


4x/10x^2+5x/10x^2-15=0

We multiply all the terms by the denominator


4x+5x-15*10x^2=0

We add all the numbers together, and all the variables

9x-15*10x^2=0

Wy multiply elements

-150x^2+9x=0

a = -150; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-150)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-150}=\frac{-18}{-300}
=3/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-150}=\frac{0}{-300}
=0
$