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27x^2+21x-4=0
a = 27; b = 21; c = -4;
Δ = b2-4ac
Δ = 212-4·27·(-4)
Δ = 873
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{97}}{2*27}=\frac{-21-3\sqrt{97}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{97}}{2*27}=\frac{-21+3\sqrt{97}}{54} $
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