4/9x+1/4x=50

Solution for 4/9x+1/4x=50 equation:

4/9x+1/4x=50

We move all terms to the left:

4/9x+1/4x-(50)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


16x/36x^2+9x/36x^2-50=0

We multiply all the terms by the denominator


16x+9x-50*36x^2=0

We add all the numbers together, and all the variables

25x-50*36x^2=0

Wy multiply elements

-1800x^2+25x=0

a = -1800; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-1800)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-1800}=\frac{-50}{-3600}
=1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-1800}=\frac{0}{-3600}
=0
$