c2-5c=3

Solution for c2-5c=3 equation:

c2-5c=3

We move all terms to the left:

c2-5c-(3)=0

We add all the numbers together, and all the variables

c^2-5c-3=0

a = 1; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·1·(-3)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{37}}{2*1}=\frac{5-\sqrt{37}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*1}=\frac{5+\sqrt{37}}{2}
$