2k^2=5k+63

Solution for 2k^2=5k+63 equation:

2k^2=5k+63

We move all terms to the left:

2k^2-(5k+63)=0

We get rid of parentheses

2k^2-5k-63=0

a = 2; b = -5; c = -63;
Δ = b2-4ac
Δ = -52-4·2·(-63)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*2}=\frac{-18}{4}
=-4+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*2}=\frac{28}{4}
=7
$