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x2-24x-288=0
We add all the numbers together, and all the variables
x^2-24x-288=0
a = 1; b = -24; c = -288;
Δ = b2-4ac
Δ = -242-4·1·(-288)
Δ = 1728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{3}}{2*1}=\frac{24-24\sqrt{3}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{3}}{2*1}=\frac{24+24\sqrt{3}}{2} $
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