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7x^2+24x-288=0
a = 7; b = 24; c = -288;
Δ = b2-4ac
Δ = 242-4·7·(-288)
Δ = 8640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{15}}{2*7}=\frac{-24-24\sqrt{15}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{15}}{2*7}=\frac{-24+24\sqrt{15}}{14} $
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