x/5x+3x/10=1

Solution for x/5x+3x/10=1 equation:

x/5x+3x/10=1

We move all terms to the left:

x/5x+3x/10-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


15x^2/50x+10x/50x-1=0

We multiply all the terms by the denominator


15x^2+10x-1*50x=0

Wy multiply elements

15x^2+10x-50x=0

We add all the numbers together, and all the variables

15x^2-40x=0

a = 15; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·15·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*15}=\frac{80}{30}
=2+2/3
$