4(20r)=1/5(420r)

Solution for 4(20r)=1/5(420r) equation:

4(20r)=1/5(420r)

We move all terms to the left:

4(20r)-(1/5(420r))=0


Domain of the equation: 5420r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

420r-(+1/5420r)=0

We get rid of parentheses

420r-1/5420r=0

We multiply all the terms by the denominator


420r*5420r-1=0

Wy multiply elements

2276400r^2-1=0

a = 2276400; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2276400·(-1)
Δ = 9105600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9105600}=\sqrt{1600*5691}=\sqrt{1600}*\sqrt{5691}=40\sqrt{5691}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5691}}{2*2276400}=\frac{0-40\sqrt{5691}}{4552800}
=-\frac{40\sqrt{5691}}{4552800}
=-\frac{\sqrt{5691}}{113820}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5691}}{2*2276400}=\frac{0+40\sqrt{5691}}{4552800}
=\frac{40\sqrt{5691}}{4552800}
=\frac{\sqrt{5691}}{113820}
$