3/5x+1/10x=9

Solution for 3/5x+1/10x=9 equation:

3/5x+1/10x=9

We move all terms to the left:

3/5x+1/10x-(9)=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 calculate fractions


30x/50x^2+5x/50x^2-9=0

We multiply all the terms by the denominator


30x+5x-9*50x^2=0

We add all the numbers together, and all the variables

35x-9*50x^2=0

Wy multiply elements

-450x^2+35x=0

a = -450; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-450)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-450}=\frac{-70}{-900}
=7/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-450}=\frac{0}{-900}
=0
$