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9x^2-110x-200=0
a = 9; b = -110; c = -200;
Δ = b2-4ac
Δ = -1102-4·9·(-200)
Δ = 19300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19300}=\sqrt{100*193}=\sqrt{100}*\sqrt{193}=10\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-10\sqrt{193}}{2*9}=\frac{110-10\sqrt{193}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+10\sqrt{193}}{2*9}=\frac{110+10\sqrt{193}}{18} $
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