4(r+80)=(1/5)(20r+400)

Solution for 4(r+80)=(1/5)(20r+400) equation:

4(r+80)=(1/5)(20r+400)

We move all terms to the left:

4(r+80)-((1/5)(20r+400))=0


Domain of the equation: 5)(20r+400))!=0

r∈R


We add all the numbers together, and all the variables

4(r+80)-((+1/5)(20r+400))=0

We multiply parentheses

4r-((+1/5)(20r+400))+320=0

We multiply parentheses ..

-((+20r^2+1/5*400))+4r+320=0

We multiply all the terms by the denominator


-((+20r^2+1+4r*5*400))+320*5*400))=0


We calculate terms in parentheses: -((+20r^2+1+4r*5*400)), so:

(+20r^2+1+4r*5*400)

We get rid of parentheses

20r^2+4r*5*400+1

Wy multiply elements

20r^2+8000r*4+1

Wy multiply elements

20r^2+32000r+1

Back to the equation:

-(20r^2+32000r+1)


We add all the numbers together, and all the variables

-(20r^2+32000r+1)=0

We get rid of parentheses

-20r^2-32000r-1=0

a = -20; b = -32000; c = -1;
Δ = b2-4ac
Δ = -320002-4·(-20)·(-1)
Δ = 1023999920
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:

$\sqrt{\Delta}=\sqrt{1023999920}=\sqrt{16*63999995}=\sqrt{16}*\sqrt{63999995}=4\sqrt{63999995}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32000)-4\sqrt{63999995}}{2*-20}=\frac{32000-4\sqrt{63999995}}{-40}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32000)+4\sqrt{63999995}}{2*-20}=\frac{32000+4\sqrt{63999995}}{-40}
$