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-6x^2+24x+18=0
a = -6; b = 24; c = +18;
Δ = b2-4ac
Δ = 242-4·(-6)·18
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*-6}=\frac{-24-12\sqrt{7}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{7}}{2*-6}=\frac{-24+12\sqrt{7}}{-12} $
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