(100+20x)/45x=x

Solution for (100+20x)/45x=x equation:

(100+20x)/45x=x

We move all terms to the left:

(100+20x)/45x-(x)=0


Domain of the equation: 45x!=0

x!=0/45

x!=0

x∈R


We add all the numbers together, and all the variables

(20x+100)/45x-x=0

We add all the numbers together, and all the variables

-1x+(20x+100)/45x=0

We multiply all the terms by the denominator


-1x*45x+(20x+100)=0

Wy multiply elements

-45x^2+(20x+100)=0

We get rid of parentheses

-45x^2+20x+100=0

a = -45; b = 20; c = +100;
Δ = b2-4ac
Δ = 202-4·(-45)·100
Δ = 18400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18400}=\sqrt{400*46}=\sqrt{400}*\sqrt{46}=20\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{46}}{2*-45}=\frac{-20-20\sqrt{46}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{46}}{2*-45}=\frac{-20+20\sqrt{46}}{-90}
$