706.5=4*3.14*(r*r)

Solution for 706.5=4*3.14*(r*r) equation:

706.5=4*3.14(r*r)

We move all terms to the left:

706.5-(4*3.14(r*r))=0

We add all the numbers together, and all the variables

-(4*3.14(+r*r))+706.5=0


We calculate terms in parentheses: -(4*3.14(+r*r)), so:

4*3.14(+r*r)

Wy multiply elements

12r^2

Back to the equation:

-(12r^2)


a = -12; b = 0; c = +706.5;
Δ = b2-4ac
Δ = 02-4·(-12)·706.5
Δ = 33912
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:

$\sqrt{\Delta}=\sqrt{33912}=\sqrt{36*942}=\sqrt{36}*\sqrt{942}=6\sqrt{942}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{942}}{2*-12}=\frac{0-6\sqrt{942}}{-24}
=-\frac{6\sqrt{942}}{-24}
=-\frac{\sqrt{942}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{942}}{2*-12}=\frac{0+6\sqrt{942}}{-24}
=\frac{6\sqrt{942}}{-24}
=\frac{\sqrt{942}}{-4}
$