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4x^2-122x+9=0
a = 4; b = -122; c = +9;
Δ = b2-4ac
Δ = -1222-4·4·9
Δ = 14740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14740}=\sqrt{4*3685}=\sqrt{4}*\sqrt{3685}=2\sqrt{3685}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-2\sqrt{3685}}{2*4}=\frac{122-2\sqrt{3685}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+2\sqrt{3685}}{2*4}=\frac{122+2\sqrt{3685}}{8} $
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