9x^2+78x+1=0

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Solution for 9x^2+78x+1=0 equation:



9x^2+78x+1=0
a = 9; b = 78; c = +1;
Δ = b2-4ac
Δ = 782-4·9·1
Δ = 6048
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:
$\sqrt{\Delta}=\sqrt{6048}=\sqrt{144*42}=\sqrt{144}*\sqrt{42}=12\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-12\sqrt{42}}{2*9}=\frac{-78-12\sqrt{42}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+12\sqrt{42}}{2*9}=\frac{-78+12\sqrt{42}}{18} $

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