5(x-1)=5/4x

Solution for 5(x-1)=5/4x equation:

5(x-1)=5/4x

We move all terms to the left:

5(x-1)-(5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

5x-(+5/4x)-5=0

We get rid of parentheses

5x-5/4x-5=0

We multiply all the terms by the denominator


5x*4x-5*4x-5=0

Wy multiply elements

20x^2-20x-5=0

a = 20; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·20·(-5)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{2}}{2*20}=\frac{20-20\sqrt{2}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{2}}{2*20}=\frac{20+20\sqrt{2}}{40}
$