13c-3c^2=5

Solution for 13c-3c^2=5 equation:

13c-3c^2=5

We move all terms to the left:

13c-3c^2-(5)=0

a = -3; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·(-3)·(-5)
Δ = 109
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{-(13)-\sqrt{109}}{2*-3}=\frac{-13-\sqrt{109}}{-6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{109}}{2*-3}=\frac{-13+\sqrt{109}}{-6}
$