(4x)/(9)=(x)/(6x)+5

Solution for (4x)/(9)=(x)/(6x)+5 equation:

(4x)/(9)=(x)/(6x)+5

We move all terms to the left:

(4x)/(9)-((x)/(6x)+5)=0


Domain of the equation: 6x+5)!=0

x∈R


We get rid of parentheses

4x/9-x/6x-5=0

We calculate fractions


24x^2/54x+(-9x)/54x-5=0

We multiply all the terms by the denominator


24x^2+(-9x)-5*54x=0

Wy multiply elements

24x^2+(-9x)-270x=0

We get rid of parentheses

24x^2-9x-270x=0

We add all the numbers together, and all the variables

24x^2-279x=0

a = 24; b = -279; c = 0;
Δ = b2-4ac
Δ = -2792-4·24·0
Δ = 77841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77841}=279$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-279)-279}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-279)+279}{2*24}=\frac{558}{48}
=11+5/8
$