c(2)=25(2)+50

Solution for c(2)=25(2)+50 equation:

c(2)=25(2)+50

We move all terms to the left:

c(2)-(25(2)+50)=0

We add all the numbers together, and all the variables

c2-302=0

We add all the numbers together, and all the variables

c^2-302=0

a = 1; b = 0; c = -302;
Δ = b2-4ac
Δ = 02-4·1·(-302)
Δ = 1208
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:

$\sqrt{\Delta}=\sqrt{1208}=\sqrt{4*302}=\sqrt{4}*\sqrt{302}=2\sqrt{302}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{302}}{2*1}=\frac{0-2\sqrt{302}}{2}
=-\frac{2\sqrt{302}}{2}
=-\sqrt{302}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{302}}{2*1}=\frac{0+2\sqrt{302}}{2}
=\frac{2\sqrt{302}}{2}
=\sqrt{302}
$