2-5k^2=-29

Solution for 2-5k^2=-29 equation:

2-5k^2=-29

We move all terms to the left:

2-5k^2-(-29)=0

We add all the numbers together, and all the variables

-5k^2+31=0

a = -5; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-5)·31
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{155}}{2*-5}=\frac{0-2\sqrt{155}}{-10}
=-\frac{2\sqrt{155}}{-10}
=-\frac{\sqrt{155}}{-5}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{155}}{2*-5}=\frac{0+2\sqrt{155}}{-10}
=\frac{2\sqrt{155}}{-10}
=\frac{\sqrt{155}}{-5}
$