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9x^2-21x+4=0
a = 9; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·9·4
Δ = 297
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{33}}{2*9}=\frac{21-3\sqrt{33}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{33}}{2*9}=\frac{21+3\sqrt{33}}{18} $
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