(100+20x)=x*45x

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

(100+20x)=x*45x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

20x-x*45x+100=0

Wy multiply elements

-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}
$