9(2x-1)13x=3

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Solution for 9(2x-1)13x=3 equation:



9(2x-1)13x=3
We move all terms to the left:
9(2x-1)13x-(3)=0
We multiply parentheses
234x^2-117x-3=0
a = 234; b = -117; c = -3;
Δ = b2-4ac
Δ = -1172-4·234·(-3)
Δ = 16497
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:
$\sqrt{\Delta}=\sqrt{16497}=\sqrt{9*1833}=\sqrt{9}*\sqrt{1833}=3\sqrt{1833}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-3\sqrt{1833}}{2*234}=\frac{117-3\sqrt{1833}}{468} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+3\sqrt{1833}}{2*234}=\frac{117+3\sqrt{1833}}{468} $

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