4c(c+5)-2c=14

Solution for 4c(c+5)-2c=14 equation:

4c(c+5)-2c=14

We move all terms to the left:

4c(c+5)-2c-(14)=0

We add all the numbers together, and all the variables

-2c+4c(c+5)-14=0

We multiply parentheses

4c^2-2c+20c-14=0

We add all the numbers together, and all the variables

4c^2+18c-14=0

a = 4; b = 18; c = -14;
Δ = b2-4ac
Δ = 182-4·4·(-14)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{137}}{2*4}=\frac{-18-2\sqrt{137}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{137}}{2*4}=\frac{-18+2\sqrt{137}}{8}
$