20(1/4x+2)=20(2/5x-1)

Solution for 20(1/4x+2)=20(2/5x-1) equation:

20(1/4x+2)=20(2/5x-1)

We move all terms to the left:

20(1/4x+2)-(20(2/5x-1))=0


Domain of the equation: 4x+2)!=0

x∈R



Domain of the equation: 5x-1))!=0

x∈R


We multiply parentheses

20x-(20(2/5x-1))+40=0

We multiply all the terms by the denominator


20x*5x+40*5x-1))-(20(2-1))=0

We add all the numbers together, and all the variables

20x*5x+40*5x-1))-(201)=0

We add all the numbers together, and all the variables

20x*5x+40*5x=0

Wy multiply elements

100x^2+200x=0

a = 100; b = 200; c = 0;
Δ = b2-4ac
Δ = 2002-4·100·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-200}{2*100}=\frac{-400}{200}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+200}{2*100}=\frac{0}{200}
=0
$