-3/2x-7=5/6x+7

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Solution for -3/2x-7=5/6x+7 equation:



-3/2x-7=5/6x+7
We move all terms to the left:
-3/2x-7-(5/6x+7)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 6x+7)!=0
x∈R
We get rid of parentheses
-3/2x-5/6x-7-7=0
We calculate fractions
(-18x)/12x^2+(-10x)/12x^2-7-7=0
We add all the numbers together, and all the variables
(-18x)/12x^2+(-10x)/12x^2-14=0
We multiply all the terms by the denominator
(-18x)+(-10x)-14*12x^2=0
Wy multiply elements
-168x^2+(-18x)+(-10x)=0
We get rid of parentheses
-168x^2-18x-10x=0
We add all the numbers together, and all the variables
-168x^2-28x=0
a = -168; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-168)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-168}=\frac{0}{-336} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-168}=\frac{56}{-336} =-1/6 $

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