(4c-1)(8+c)=0

Solution for (4c-1)(8+c)=0 equation:

(4c-1)(8+c)=0

We add all the numbers together, and all the variables

(4c-1)(c+8)=0

We multiply parentheses ..

(+4c^2+32c-1c-8)=0

We get rid of parentheses

4c^2+32c-1c-8=0

We add all the numbers together, and all the variables

4c^2+31c-8=0

a = 4; b = 31; c = -8;
Δ = b2-4ac
Δ = 312-4·4·(-8)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-33}{2*4}=\frac{-64}{8}
=-8
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+33}{2*4}=\frac{2}{8}
=1/4
$