x(1+25/100)=5x/4

Solution for x(1+25/100)=5x/4 equation:

x(1+25/100)=5x/4

We move all terms to the left:

x(1+25/100)-(5x/4)=0

We add all the numbers together, and all the variables

x(25/100+1)-(+5x/4)=0

We multiply parentheses

25x^2+x-(+5x/4)=0

We get rid of parentheses

25x^2+x-5x/4=0

We multiply all the terms by the denominator


25x^2*4+x*4-5x=0

We add all the numbers together, and all the variables

25x^2*4-5x+x*4=0

Wy multiply elements

100x^2-5x+4x=0

We add all the numbers together, and all the variables

100x^2-1x=0

a = 100; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·100·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*100}=\frac{0}{200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*100}=\frac{2}{200}
=1/100
$