9x^2-15x-3=0

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Solution for 9x^2-15x-3=0 equation:



9x^2-15x-3=0
a = 9; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·9·(-3)
Δ = 333
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:
$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{37}}{2*9}=\frac{15-3\sqrt{37}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{37}}{2*9}=\frac{15+3\sqrt{37}}{18} $

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