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-12x^2-24x+9=0
a = -12; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·(-12)·9
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{7}}{2*-12}=\frac{24-12\sqrt{7}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{7}}{2*-12}=\frac{24+12\sqrt{7}}{-24} $
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