2x-10=1/3x-3

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Solution for 2x-10=1/3x-3 equation:



2x-10=1/3x-3
We move all terms to the left:
2x-10-(1/3x-3)=0
Domain of the equation: 3x-3)!=0
x∈R
We get rid of parentheses
2x-1/3x+3-10=0
We multiply all the terms by the denominator
2x*3x+3*3x-10*3x-1=0
Wy multiply elements
6x^2+9x-30x-1=0
We add all the numbers together, and all the variables
6x^2-21x-1=0
a = 6; b = -21; c = -1;
Δ = b2-4ac
Δ = -212-4·6·(-1)
Δ = 465
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{-(-21)-\sqrt{465}}{2*6}=\frac{21-\sqrt{465}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*6}=\frac{21+\sqrt{465}}{12} $

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