2k^2-63=11k

Solution for 2k^2-63=11k equation:

2k^2-63=11k

We move all terms to the left:

2k^2-63-(11k)=0

a = 2; b = -11; c = -63;
Δ = b2-4ac
Δ = -112-4·2·(-63)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*2}=\frac{-14}{4}
=-3+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*2}=\frac{36}{4}
=9
$