4/9x+1/4x=75

Solution for 4/9x+1/4x=75 equation:

4/9x+1/4x=75

We move all terms to the left:

4/9x+1/4x-(75)=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^2-75=0

We multiply all the terms by the denominator


16x+9x-75*36x^2=0

We add all the numbers together, and all the variables

25x-75*36x^2=0

Wy multiply elements

-2700x^2+25x=0

a = -2700; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-2700)·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*-2700}=\frac{-50}{-5400}
=1/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-2700}=\frac{0}{-5400}
=0
$