c/502+1202=c2

Solution for c/502+1202=c2 equation:

c/502+1202=c2

We move all terms to the left:

c/502+1202-(c2)=0

We add all the numbers together, and all the variables

-1c^2+c/502+1202=0

We multiply all the terms by the denominator


-1c^2*502+c+1202*502=0

We add all the numbers together, and all the variables

-1c^2*502+c+603404=0

Wy multiply elements

-502c^2+c+603404=0

a = -502; b = 1; c = +603404;
Δ = b2-4ac
Δ = 12-4·(-502)·603404
Δ = 1211635233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1211635233}=\sqrt{9*134626137}=\sqrt{9}*\sqrt{134626137}=3\sqrt{134626137}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{134626137}}{2*-502}=\frac{-1-3\sqrt{134626137}}{-1004}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{134626137}}{2*-502}=\frac{-1+3\sqrt{134626137}}{-1004}
$