4(x-9)=4(+1/9x)

Solution for 4(x-9)=4(+1/9x) equation:

4(x-9)=4(+1/9x)

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We multiply parentheses

4x-(4(+1/9x))-36=0

We multiply all the terms by the denominator


4x*9x))-(4(-36*9x))+1=0

Wy multiply elements

36x^2-324x=0

a = 36; b = -324; c = 0;
Δ = b2-4ac
Δ = -3242-4·36·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-324}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+324}{2*36}=\frac{648}{72}
=9
$