-x+3/2x=-6

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



-x+3/2x=-6
We move all terms to the left:
-x+3/2x-(-6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+3/2x+6=0
We multiply all the terms by the denominator
-1x*2x+6*2x+3=0
Wy multiply elements
-2x^2+12x+3=0
a = -2; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-2)·3
Δ = 168
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:
$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*-2}=\frac{-12-2\sqrt{42}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*-2}=\frac{-12+2\sqrt{42}}{-4} $

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