x-9=37/100*x

Solution for x-9=37/100*x equation:

x-9=37/100x

We move all terms to the left:

x-9-(37/100x)=0


Domain of the equation: 100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+37/100x)-9=0

We get rid of parentheses

x-37/100x-9=0

We multiply all the terms by the denominator


x*100x-9*100x-37=0

Wy multiply elements

100x^2-900x-37=0

a = 100; b = -900; c = -37;
Δ = b2-4ac
Δ = -9002-4·100·(-37)
Δ = 824800
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:

$\sqrt{\Delta}=\sqrt{824800}=\sqrt{400*2062}=\sqrt{400}*\sqrt{2062}=20\sqrt{2062}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-20\sqrt{2062}}{2*100}=\frac{900-20\sqrt{2062}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+20\sqrt{2062}}{2*100}=\frac{900+20\sqrt{2062}}{200}
$