V(r)=50018(0.25-r^2)

Solution for V(r)=50018(0.25-r^2) equation:

(V)=50018(0.25-V^2)

We move all terms to the left:

(V)-(50018(0.25-V^2))=0


We calculate terms in parentheses: -(50018(0.25-V^2)), so:

50018(0.25-V^2)

We multiply parentheses

-50018V^2+12504.5

Back to the equation:

-(-50018V^2+12504.5)


We get rid of parentheses

50018V^2+V-12504.5=0

a = 50018; b = 1; c = -12504.5;
Δ = b2-4ac
Δ = 12-4·50018·(-12504.5)
Δ = 2501800325
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2501800325}=\sqrt{25*100072013}=\sqrt{25}*\sqrt{100072013}=5\sqrt{100072013}$
$V_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{100072013}}{2*50018}=\frac{-1-5\sqrt{100072013}}{100036}
$
$V_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{100072013}}{2*50018}=\frac{-1+5\sqrt{100072013}}{100036}
$