5/6x-4-6x+2=-3

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Solution for 5/6x-4-6x+2=-3 equation:



5/6x-4-6x+2=-3
We move all terms to the left:
5/6x-4-6x+2-(-3)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We add all the numbers together, and all the variables
-6x+5/6x+1=0
We multiply all the terms by the denominator
-6x*6x+1*6x+5=0
Wy multiply elements
-36x^2+6x+5=0
a = -36; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-36)·5
Δ = 756
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:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{21}}{2*-36}=\frac{-6-6\sqrt{21}}{-72} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{21}}{2*-36}=\frac{-6+6\sqrt{21}}{-72} $

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