2k^2-32k=58

Solution for 2k^2-32k=58 equation:

2k^2-32k=58

We move all terms to the left:

2k^2-32k-(58)=0

a = 2; b = -32; c = -58;
Δ = b2-4ac
Δ = -322-4·2·(-58)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{93}}{2*2}=\frac{32-4\sqrt{93}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{93}}{2*2}=\frac{32+4\sqrt{93}}{4}
$