1/3x=2x-15

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Solution for 1/3x=2x-15 equation:



1/3x=2x-15
We move all terms to the left:
1/3x-(2x-15)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We get rid of parentheses
1/3x-2x+15=0
We multiply all the terms by the denominator
-2x*3x+15*3x+1=0
Wy multiply elements
-6x^2+45x+1=0
a = -6; b = 45; c = +1;
Δ = b2-4ac
Δ = 452-4·(-6)·1
Δ = 2049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2049}}{2*-6}=\frac{-45-\sqrt{2049}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2049}}{2*-6}=\frac{-45+\sqrt{2049}}{-12} $

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