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3x(x+6)=24
We move all terms to the left:
3x(x+6)-(24)=0
We multiply parentheses
3x^2+18x-24=0
a = 3; b = 18; c = -24;
Δ = b2-4ac
Δ = 182-4·3·(-24)
Δ = 612
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{17}}{2*3}=\frac{-18-6\sqrt{17}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{17}}{2*3}=\frac{-18+6\sqrt{17}}{6} $
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