5c^2-17c=-14

Solution for 5c^2-17c=-14 equation:

5c^2-17c=-14

We move all terms to the left:

5c^2-17c-(-14)=0

We add all the numbers together, and all the variables

5c^2-17c+14=0

a = 5; b = -17; c = +14;
Δ = b2-4ac
Δ = -172-4·5·14
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3}{2*5}=\frac{14}{10}
=1+2/5
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3}{2*5}=\frac{20}{10}
=2
$