2k^2-4k=15

Solution for 2k^2-4k=15 equation:

2k^2-4k=15

We move all terms to the left:

2k^2-4k-(15)=0

a = 2; b = -4; c = -15;
Δ = b2-4ac
Δ = -42-4·2·(-15)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*2}=\frac{4-2\sqrt{34}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*2}=\frac{4+2\sqrt{34}}{4}
$