1/2x-1/4=2/9x+6

Solution for 1/2x-1/4=2/9x+6 equation:

1/2x-1/4=2/9x+6

We move all terms to the left:

1/2x-1/4-(2/9x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x+6)!=0

x∈R


We get rid of parentheses

1/2x-2/9x-6-1/4=0

We calculate fractions


(-162x^2)/288x^2+144x/288x^2+(-64x)/288x^2-6=0

We multiply all the terms by the denominator


(-162x^2)+144x+(-64x)-6*288x^2=0

Wy multiply elements

(-162x^2)-1728x^2+144x+(-64x)=0

We get rid of parentheses

-162x^2-1728x^2+144x-64x=0

We add all the numbers together, and all the variables

-1890x^2+80x=0

a = -1890; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-1890)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-1890}=\frac{-160}{-3780}
=8/189
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-1890}=\frac{0}{-3780}
=0
$