3/9x+1/5x=69

Solution for 3/9x+1/5x=69 equation:

3/9x+1/5x=69

We move all terms to the left:

3/9x+1/5x-(69)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


15x/45x^2+9x/45x^2-69=0

We multiply all the terms by the denominator


15x+9x-69*45x^2=0

We add all the numbers together, and all the variables

24x-69*45x^2=0

Wy multiply elements

-3105x^2+24x=0

a = -3105; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-3105)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-3105}=\frac{-48}{-6210}
=8/1035
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-3105}=\frac{0}{-6210}
=0
$