1/2x+3=6x+-8

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Solution for 1/2x+3=6x+-8 equation:



1/2x+3=6x+-8
We move all terms to the left:
1/2x+3-(6x+-8)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(6x-8)+3=0
We get rid of parentheses
1/2x-6x+8+3=0
We multiply all the terms by the denominator
-6x*2x+8*2x+3*2x+1=0
Wy multiply elements
-12x^2+16x+6x+1=0
We add all the numbers together, and all the variables
-12x^2+22x+1=0
a = -12; b = 22; c = +1;
Δ = b2-4ac
Δ = 222-4·(-12)·1
Δ = 532
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:
$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{133}}{2*-12}=\frac{-22-2\sqrt{133}}{-24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{133}}{2*-12}=\frac{-22+2\sqrt{133}}{-24} $

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