(13c-8)(5c+11)=0

Solution for (13c-8)(5c+11)=0 equation:

(13c-8)(5c+11)=0

We multiply parentheses ..

(+65c^2+143c-40c-88)=0

We get rid of parentheses

65c^2+143c-40c-88=0

We add all the numbers together, and all the variables

65c^2+103c-88=0

a = 65; b = 103; c = -88;
Δ = b2-4ac
Δ = 1032-4·65·(-88)
Δ = 33489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33489}=183$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-183}{2*65}=\frac{-286}{130}
=-2+1/5
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+183}{2*65}=\frac{80}{130}
=8/13
$