9x^2+27x-172=0

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Solution for 9x^2+27x-172=0 equation:



9x^2+27x-172=0
a = 9; b = 27; c = -172;
Δ = b2-4ac
Δ = 272-4·9·(-172)
Δ = 6921
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:
$\sqrt{\Delta}=\sqrt{6921}=\sqrt{9*769}=\sqrt{9}*\sqrt{769}=3\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{769}}{2*9}=\frac{-27-3\sqrt{769}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{769}}{2*9}=\frac{-27+3\sqrt{769}}{18} $

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