750=2*3.14*r*50+2*3.14*(r*r)

Solution for 750=2*3.14*r*50+2*3.14*(r*r) equation:

750=2*3.14r*50+2*3.14(r*r)

We move all terms to the left:

750-(2*3.14r*50+2*3.14(r*r))=0

We add all the numbers together, and all the variables

-(2*3.14r*50+2*3.14(+r*r))+750=0


We calculate terms in parentheses: -(2*3.14r*50+2*3.14(+r*r)), so:

2*3.14r*50+2*3.14(+r*r)

Wy multiply elements

6r^2+300r

Back to the equation:

-(6r^2+300r)


We get rid of parentheses

-6r^2-300r+750=0

a = -6; b = -300; c = +750;
Δ = b2-4ac
Δ = -3002-4·(-6)·750
Δ = 108000
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:

$\sqrt{\Delta}=\sqrt{108000}=\sqrt{3600*30}=\sqrt{3600}*\sqrt{30}=60\sqrt{30}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-60\sqrt{30}}{2*-6}=\frac{300-60\sqrt{30}}{-12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+60\sqrt{30}}{2*-6}=\frac{300+60\sqrt{30}}{-12}
$