5(c-8)-3(c2+12)=-84

Solution for 5(c-8)-3(c2+12)=-84 equation:

5(c-8)-3(c2+12)=-84

We move all terms to the left:

5(c-8)-3(c2+12)-(-84)=0

We add all the numbers together, and all the variables

-3(+c^2+12)+5(c-8)-(-84)=0

We add all the numbers together, and all the variables

-3(+c^2+12)+5(c-8)+84=0

We multiply parentheses

-3c^2+5c-36-40+84=0

We add all the numbers together, and all the variables

-3c^2+5c+8=0

a = -3; b = 5; c = +8;
Δ = b2-4ac
Δ = 52-4·(-3)·8
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-3}=\frac{6}{-6}
=-1
$