20k2-81=-40

Solution for 20k2-81=-40 equation:

20k^2-81=-40

We move all terms to the left:

20k^2-81-(-40)=0

We add all the numbers together, and all the variables

20k^2-41=0

a = 20; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·20·(-41)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{205}}{2*20}=\frac{0-4\sqrt{205}}{40}
=-\frac{4\sqrt{205}}{40}
=-\frac{\sqrt{205}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{205}}{2*20}=\frac{0+4\sqrt{205}}{40}
=\frac{4\sqrt{205}}{40}
=\frac{\sqrt{205}}{10}
$