c^2=24c-5

Solution for c^2=24c-5 equation:

c^2=24c-5

We move all terms to the left:

c^2-(24c-5)=0

We get rid of parentheses

c^2-24c+5=0

a = 1; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·1·5
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{139}}{2*1}=\frac{24-2\sqrt{139}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{139}}{2*1}=\frac{24+2\sqrt{139}}{2}
$