2k^2+1=183

Solution for 2k^2+1=183 equation:

2k^2+1=183

We move all terms to the left:

2k^2+1-(183)=0

We add all the numbers together, and all the variables

2k^2-182=0

a = 2; b = 0; c = -182;
Δ = b2-4ac
Δ = 02-4·2·(-182)
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{91}}{2*2}=\frac{0-4\sqrt{91}}{4}
=-\frac{4\sqrt{91}}{4}
=-\sqrt{91}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{91}}{2*2}=\frac{0+4\sqrt{91}}{4}
=\frac{4\sqrt{91}}{4}
=\sqrt{91}
$