x/9x=4x+20

Solution for x/9x=4x+20 equation:

x/9x=4x+20

We move all terms to the left:

x/9x-(4x+20)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

x/9x-4x-20=0

We multiply all the terms by the denominator


x-4x*9x-20*9x=0

Wy multiply elements

-36x^2+x-180x=0

We add all the numbers together, and all the variables

-36x^2-179x=0

a = -36; b = -179; c = 0;
Δ = b2-4ac
Δ = -1792-4·(-36)·0
Δ = 32041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32041}=179$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-179}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+179}{2*-36}=\frac{358}{-72}
=-4+35/36
$