c^2+5c=3

Solution for c^2+5c=3 equation:

c^2+5c=3

We move all terms to the left:

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}
$