g=9.81*50/0.5^2

Solution for g=9.81*50/0.5^2 equation:

g=9.81*50/0.5^2

We move all terms to the left:

g-(9.81*50/0.5^2)=0

We get rid of parentheses

g-9.81*50/0.5^2=0

We multiply all the terms by the denominator


g*0.5^2-9.81*50=0

We add all the numbers together, and all the variables

g*0.5^2-490.5=0

Wy multiply elements

0g^2-490.5=0

We add all the numbers together, and all the variables

g^2-490.5=0

a = 1; b = 0; c = -490.5;
Δ = b2-4ac
Δ = 02-4·1·(-490.5)
Δ = 1962
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1962}=\sqrt{9*218}=\sqrt{9}*\sqrt{218}=3\sqrt{218}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{218}}{2*1}=\frac{0-3\sqrt{218}}{2}
=-\frac{3\sqrt{218}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{218}}{2*1}=\frac{0+3\sqrt{218}}{2}
=\frac{3\sqrt{218}}{2}
$