14-(3c+2)c=2.5

Solution for 14-(3c+2)c=2.5 equation:

14-(3c+2)c=2.5

We move all terms to the left:

14-(3c+2)c-(2.5)=0

We add all the numbers together, and all the variables

-(3c+2)c+11.5=0

We multiply parentheses

-3c^2-2c+11.5=0

a = -3; b = -2; c = +11.5;
Δ = b2-4ac
Δ = -22-4·(-3)·11.5
Δ = 142
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{-(-2)-\sqrt{142}}{2*-3}=\frac{2-\sqrt{142}}{-6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{142}}{2*-3}=\frac{2+\sqrt{142}}{-6}
$