9x(3x-1)=15

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Solution for 9x(3x-1)=15 equation:



9x(3x-1)=15
We move all terms to the left:
9x(3x-1)-(15)=0
We multiply parentheses
27x^2-9x-15=0
a = 27; b = -9; c = -15;
Δ = b2-4ac
Δ = -92-4·27·(-15)
Δ = 1701
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:
$\sqrt{\Delta}=\sqrt{1701}=\sqrt{81*21}=\sqrt{81}*\sqrt{21}=9\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{21}}{2*27}=\frac{9-9\sqrt{21}}{54} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{21}}{2*27}=\frac{9+9\sqrt{21}}{54} $

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