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3x^2-126x-189=0
a = 3; b = -126; c = -189;
Δ = b2-4ac
Δ = -1262-4·3·(-189)
Δ = 18144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18144}=\sqrt{1296*14}=\sqrt{1296}*\sqrt{14}=36\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-36\sqrt{14}}{2*3}=\frac{126-36\sqrt{14}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+36\sqrt{14}}{2*3}=\frac{126+36\sqrt{14}}{6} $
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