2x+6=6(5/6x-3)

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Solution for 2x+6=6(5/6x-3) equation:



2x+6=6(5/6x-3)
We move all terms to the left:
2x+6-(6(5/6x-3))=0
Domain of the equation: 6x-3))!=0
x∈R
We multiply all the terms by the denominator
2x*6x+6*6x-3))-(6(5-3))=0
We add all the numbers together, and all the variables
2x*6x+6*6x-3))-(62)=0
We add all the numbers together, and all the variables
2x*6x+6*6x=0
Wy multiply elements
12x^2+36x=0
a = 12; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·12·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*12}=\frac{-72}{24} =-3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*12}=\frac{0}{24} =0 $

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