64k^2-76k-140=0

Solution for 64k^2-76k-140=0 equation:

64k^2-76k-140=0

a = 64; b = -76; c = -140;
Δ = b2-4ac
Δ = -762-4·64·(-140)
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-204}{2*64}=\frac{-128}{128}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+204}{2*64}=\frac{280}{128}
=2+3/16
$