4c^2+10c=-4

Solution for 4c^2+10c=-4 equation:

4c^2+10c=-4

We move all terms to the left:

4c^2+10c-(-4)=0

We add all the numbers together, and all the variables

4c^2+10c+4=0

a = 4; b = 10; c = +4;
Δ = b2-4ac
Δ = 102-4·4·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6}{2*4}=\frac{-16}{8}
=-2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6}{2*4}=\frac{-4}{8}
=-1/2
$