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4k^2+14k+9=0
a = 4; b = 14; c = +9;
Δ = b2-4ac
Δ = 142-4·4·9
Δ = 52
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{13}}{2*4}=\frac{-14-2\sqrt{13}}{8} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{13}}{2*4}=\frac{-14+2\sqrt{13}}{8} $
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