2/9x+1/5x=32

Solution for 2/9x+1/5x=32 equation:

2/9x+1/5x=32

We move all terms to the left:

2/9x+1/5x-(32)=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


10x/45x^2+9x/45x^2-32=0

We multiply all the terms by the denominator


10x+9x-32*45x^2=0

We add all the numbers together, and all the variables

19x-32*45x^2=0

Wy multiply elements

-1440x^2+19x=0

a = -1440; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-1440)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-1440}=\frac{-38}{-2880}
=19/1440
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-1440}=\frac{0}{-2880}
=0
$