5/2x+6=30/4x+8

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Solution for 5/2x+6=30/4x+8 equation:



5/2x+6=30/4x+8
We move all terms to the left:
5/2x+6-(30/4x+8)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x+8)!=0
x∈R
We get rid of parentheses
5/2x-30/4x-8+6=0
We calculate fractions
20x/8x^2+(-60x)/8x^2-8+6=0
We add all the numbers together, and all the variables
20x/8x^2+(-60x)/8x^2-2=0
We multiply all the terms by the denominator
20x+(-60x)-2*8x^2=0
Wy multiply elements
-16x^2+20x+(-60x)=0
We get rid of parentheses
-16x^2+20x-60x=0
We add all the numbers together, and all the variables
-16x^2-40x=0
a = -16; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-16)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-16}=\frac{0}{-32} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-16}=\frac{80}{-32} =-2+1/2 $

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