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9x^2-330x+180=0
a = 9; b = -330; c = +180;
Δ = b2-4ac
Δ = -3302-4·9·180
Δ = 102420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{102420}=\sqrt{36*2845}=\sqrt{36}*\sqrt{2845}=6\sqrt{2845}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-6\sqrt{2845}}{2*9}=\frac{330-6\sqrt{2845}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+6\sqrt{2845}}{2*9}=\frac{330+6\sqrt{2845}}{18} $
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