4x/9x-8x-5=20

Solution for 4x/9x-8x-5=20 equation:

4x/9x-8x-5=20

We move all terms to the left:

4x/9x-8x-5-(20)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-8x+4x/9x-25=0

We multiply all the terms by the denominator


-8x*9x+4x-25*9x=0

We add all the numbers together, and all the variables

4x-8x*9x-25*9x=0

Wy multiply elements

-72x^2+4x-225x=0

We add all the numbers together, and all the variables

-72x^2-221x=0

a = -72; b = -221; c = 0;
Δ = b2-4ac
Δ = -2212-4·(-72)·0
Δ = 48841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48841}=221$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-221)-221}{2*-72}=\frac{0}{-144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-221)+221}{2*-72}=\frac{442}{-144}
=-3+5/72
$