32k^2-12k-77=0

Solution for 32k^2-12k-77=0 equation:

32k^2-12k-77=0

a = 32; b = -12; c = -77;
Δ = b2-4ac
Δ = -122-4·32·(-77)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-100}{2*32}=\frac{-88}{64}
=-1+3/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+100}{2*32}=\frac{112}{64}
=1+3/4
$