4(x-9)=4(+1/5x)

Solution for 4(x-9)=4(+1/5x) equation:

4(x-9)=4(+1/5x)

We move all terms to the left:

4(x-9)-(4(+1/5x))=0


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

x!=0/1

x!=0

x∈R


We multiply parentheses

4x-(4(+1/5x))-36=0

We multiply all the terms by the denominator


4x*5x))-(4(-36*5x))+1=0

Wy multiply elements

20x^2-180x=0

a = 20; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·20·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*20}=\frac{360}{40}
=9
$