(5x-1)3x=54

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Solution for (5x-1)3x=54 equation:



(5x-1)3x=54
We move all terms to the left:
(5x-1)3x-(54)=0
We multiply parentheses
15x^2-3x-54=0
a = 15; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·15·(-54)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-57}{2*15}=\frac{-54}{30} =-1+4/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+57}{2*15}=\frac{60}{30} =2 $

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