8k^2+20k-57=0

Solution for 8k^2+20k-57=0 equation:

8k^2+20k-57=0

a = 8; b = 20; c = -57;
Δ = b2-4ac
Δ = 202-4·8·(-57)
Δ = 2224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2224}=\sqrt{16*139}=\sqrt{16}*\sqrt{139}=4\sqrt{139}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{139}}{2*8}=\frac{-20-4\sqrt{139}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{139}}{2*8}=\frac{-20+4\sqrt{139}}{16}
$