1/3x-10=4x

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Solution for 1/3x-10=4x equation:



1/3x-10=4x
We move all terms to the left:
1/3x-10-(4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
-4x+1/3x-10=0
We multiply all the terms by the denominator
-4x*3x-10*3x+1=0
Wy multiply elements
-12x^2-30x+1=0
a = -12; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-12)·1
Δ = 948
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:
$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{237}}{2*-12}=\frac{30-2\sqrt{237}}{-24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{237}}{2*-12}=\frac{30+2\sqrt{237}}{-24} $

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