2k^2-7k-32=-11

Solution for 2k^2-7k-32=-11 equation:

2k^2-7k-32=-11

We move all terms to the left:

2k^2-7k-32-(-11)=0

We add all the numbers together, and all the variables

2k^2-7k-21=0

a = 2; b = -7; c = -21;
Δ = b2-4ac
Δ = -72-4·2·(-21)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{217}}{2*2}=\frac{7-\sqrt{217}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{217}}{2*2}=\frac{7+\sqrt{217}}{4}
$