22/7*r^2=100

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

22/7r^2=100

We move all terms to the left:

22/7r^2-(100)=0


Domain of the equation: 7r^2!=0

r^2!=0/7

r^2!=√0

r!=0

r∈R


We multiply all the terms by the denominator


-100*7r^2+22=0

Wy multiply elements

-700r^2+22=0

a = -700; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-700)·22
Δ = 61600
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:

$\sqrt{\Delta}=\sqrt{61600}=\sqrt{400*154}=\sqrt{400}*\sqrt{154}=20\sqrt{154}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{154}}{2*-700}=\frac{0-20\sqrt{154}}{-1400}
=-\frac{20\sqrt{154}}{-1400}
=-\frac{\sqrt{154}}{-70}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{154}}{2*-700}=\frac{0+20\sqrt{154}}{-1400}
=\frac{20\sqrt{154}}{-1400}
=\frac{\sqrt{154}}{-70}
$