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6x^2+22x+9=0
a = 6; b = 22; c = +9;
Δ = b2-4ac
Δ = 222-4·6·9
Δ = 268
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{67}}{2*6}=\frac{-22-2\sqrt{67}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{67}}{2*6}=\frac{-22+2\sqrt{67}}{12} $
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