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9x^2-180x-63=0
a = 9; b = -180; c = -63;
Δ = b2-4ac
Δ = -1802-4·9·(-63)
Δ = 34668
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34668}=\sqrt{324*107}=\sqrt{324}*\sqrt{107}=18\sqrt{107}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-18\sqrt{107}}{2*9}=\frac{180-18\sqrt{107}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+18\sqrt{107}}{2*9}=\frac{180+18\sqrt{107}}{18} $
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