4/9x+1/5x=55

Solution for 4/9x+1/5x=55 equation:

4/9x+1/5x=55

We move all terms to the left:

4/9x+1/5x-(55)=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


20x/45x^2+9x/45x^2-55=0

We multiply all the terms by the denominator


20x+9x-55*45x^2=0

We add all the numbers together, and all the variables

29x-55*45x^2=0

Wy multiply elements

-2475x^2+29x=0

a = -2475; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-2475)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-2475}=\frac{-58}{-4950}
=29/2475
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-2475}=\frac{0}{-4950}
=0
$