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9x^2-288x-784=0
a = 9; b = -288; c = -784;
Δ = b2-4ac
Δ = -2882-4·9·(-784)
Δ = 111168
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{111168}=\sqrt{576*193}=\sqrt{576}*\sqrt{193}=24\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-24\sqrt{193}}{2*9}=\frac{288-24\sqrt{193}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+24\sqrt{193}}{2*9}=\frac{288+24\sqrt{193}}{18} $
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