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5k2+9=20

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Solution for 5k2+9=20 equation:



5k^2+9=20
We move all terms to the left:
5k^2+9-(20)=0
We add all the numbers together, and all the variables
5k^2-11=0
a = 5; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·5·(-11)
Δ = 220
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{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}
k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{55}}{2*5}=\frac{0-2\sqrt{55}}{10} =-\frac{2\sqrt{55}}{10} =-\frac{\sqrt{55}}{5}
k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{55}}{2*5}=\frac{0+2\sqrt{55}}{10} =\frac{2\sqrt{55}}{10} =\frac{\sqrt{55}}{5}

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