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

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



3/4x-6+2/3x+-6=-4
We move all terms to the left:
3/4x-6+2/3x+-6-(-4)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
3/4x+2/3x-8=0
We calculate fractions
9x/12x^2+8x/12x^2-8=0
We multiply all the terms by the denominator
9x+8x-8*12x^2=0
We add all the numbers together, and all the variables
17x-8*12x^2=0
Wy multiply elements
-96x^2+17x=0
a = -96; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-96)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-96}=\frac{-34}{-192} =17/96 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-96}=\frac{0}{-192} =0 $

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