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9x^2+30x+17=0
a = 9; b = 30; c = +17;
Δ = b2-4ac
Δ = 302-4·9·17
Δ = 288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{2}}{2*9}=\frac{-30-12\sqrt{2}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{2}}{2*9}=\frac{-30+12\sqrt{2}}{18} $
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