(5+3c)(6c-8)=14

Solution for (5+3c)(6c-8)=14 equation:

(5+3c)(6c-8)=14

We move all terms to the left:

(5+3c)(6c-8)-(14)=0

We add all the numbers together, and all the variables

(3c+5)(6c-8)-14=0

We multiply parentheses ..

(+18c^2-24c+30c-40)-14=0

We get rid of parentheses

18c^2-24c+30c-40-14=0

We add all the numbers together, and all the variables

18c^2+6c-54=0

a = 18; b = 6; c = -54;
Δ = b2-4ac
Δ = 62-4·18·(-54)
Δ = 3924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{36*109}=\sqrt{36}*\sqrt{109}=6\sqrt{109}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{109}}{2*18}=\frac{-6-6\sqrt{109}}{36}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{109}}{2*18}=\frac{-6+6\sqrt{109}}{36}
$