3/4x-5=2/3x+7

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Solution for 3/4x-5=2/3x+7 equation:



3/4x-5=2/3x+7
We move all terms to the left:
3/4x-5-(2/3x+7)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x+7)!=0
x∈R
We get rid of parentheses
3/4x-2/3x-7-5=0
We calculate fractions
9x/12x^2+(-8x)/12x^2-7-5=0
We add all the numbers together, and all the variables
9x/12x^2+(-8x)/12x^2-12=0
We multiply all the terms by the denominator
9x+(-8x)-12*12x^2=0
Wy multiply elements
-144x^2+9x+(-8x)=0
We get rid of parentheses
-144x^2+9x-8x=0
We add all the numbers together, and all the variables
-144x^2+x=0
a = -144; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-144)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-144}=\frac{-2}{-288} =1/144 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-144}=\frac{0}{-288} =0 $

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