4/9x-1/4x=11

Solution for 4/9x-1/4x=11 equation:

4/9x-1/4x=11

We move all terms to the left:

4/9x-1/4x-(11)=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^2-11=0

We multiply all the terms by the denominator


16x+(-9x)-11*36x^2=0

Wy multiply elements

-396x^2+16x+(-9x)=0

We get rid of parentheses

-396x^2+16x-9x=0

We add all the numbers together, and all the variables

-396x^2+7x=0

a = -396; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-396)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-396}=\frac{-14}{-792}
=7/396
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-396}=\frac{0}{-792}
=0
$