2*22/7*r+8r=100

Solution for 2*22/7*r+8r=100 equation:

2*22/7r+8r=100

We move all terms to the left:

2*22/7r+8r-(100)=0


Domain of the equation: 7r!=0

r!=0/7

r!=0

r∈R


We add all the numbers together, and all the variables

8r+2*22/7r-100=0

We multiply all the terms by the denominator


8r*7r-100*7r+2*22=0

We add all the numbers together, and all the variables

8r*7r-100*7r+44=0

Wy multiply elements

56r^2-700r+44=0

a = 56; b = -700; c = +44;
Δ = b2-4ac
Δ = -7002-4·56·44
Δ = 480144
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:

$\sqrt{\Delta}=\sqrt{480144}=\sqrt{16*30009}=\sqrt{16}*\sqrt{30009}=4\sqrt{30009}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-4\sqrt{30009}}{2*56}=\frac{700-4\sqrt{30009}}{112}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+4\sqrt{30009}}{2*56}=\frac{700+4\sqrt{30009}}{112}
$