35k^2+51k-8=0

Solution for 35k^2+51k-8=0 equation:

35k^2+51k-8=0

a = 35; b = 51; c = -8;
Δ = b2-4ac
Δ = 512-4·35·(-8)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-61}{2*35}=\frac{-112}{70}
=-1+3/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+61}{2*35}=\frac{10}{70}
=1/7
$