x-64=(36)/(100)x

Solution for x-64=(36)/(100)x equation:

x-64=(36)/(100)x

We move all terms to the left:

x-64-((36)/(100)x)=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-(+36/100x)-64=0

We get rid of parentheses

x-36/100x-64=0

We multiply all the terms by the denominator


x*100x-64*100x-36=0

Wy multiply elements

100x^2-6400x-36=0

a = 100; b = -6400; c = -36;
Δ = b2-4ac
Δ = -64002-4·100·(-36)
Δ = 40974400
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:

$\sqrt{\Delta}=\sqrt{40974400}=\sqrt{1600*25609}=\sqrt{1600}*\sqrt{25609}=40\sqrt{25609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6400)-40\sqrt{25609}}{2*100}=\frac{6400-40\sqrt{25609}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6400)+40\sqrt{25609}}{2*100}=\frac{6400+40\sqrt{25609}}{200}
$