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6x(x+4)=24=2x^32
We move all terms to the left:
6x(x+4)-(24)=0
We multiply parentheses
6x^2+24x-24=0
a = 6; b = 24; c = -24;
Δ = b2-4ac
Δ = 242-4·6·(-24)
Δ = 1152
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{2}}{2*6}=\frac{-24-24\sqrt{2}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{2}}{2*6}=\frac{-24+24\sqrt{2}}{12} $
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