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4k^2-18k-27=0
a = 4; b = -18; c = -27;
Δ = b2-4ac
Δ = -182-4·4·(-27)
Δ = 756
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{21}}{2*4}=\frac{18-6\sqrt{21}}{8} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{21}}{2*4}=\frac{18+6\sqrt{21}}{8} $
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