22/7*r^2=490

Solution for 22/7*r^2=490 equation:

22/7r^2=490

We move all terms to the left:

22/7r^2-(490)=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


-490*7r^2+22=0

Wy multiply elements

-3430r^2+22=0

a = -3430; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-3430)·22
Δ = 301840
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:

$\sqrt{\Delta}=\sqrt{301840}=\sqrt{784*385}=\sqrt{784}*\sqrt{385}=28\sqrt{385}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{385}}{2*-3430}=\frac{0-28\sqrt{385}}{-6860}
=-\frac{28\sqrt{385}}{-6860}
=-\frac{\sqrt{385}}{-245}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{385}}{2*-3430}=\frac{0+28\sqrt{385}}{-6860}
=\frac{28\sqrt{385}}{-6860}
=\frac{\sqrt{385}}{-245}
$