3/2x-4=1/4x+6

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Solution for 3/2x-4=1/4x+6 equation:



3/2x-4=1/4x+6
We move all terms to the left:
3/2x-4-(1/4x+6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x+6)!=0
x∈R
We get rid of parentheses
3/2x-1/4x-6-4=0
We calculate fractions
12x/8x^2+(-2x)/8x^2-6-4=0
We add all the numbers together, and all the variables
12x/8x^2+(-2x)/8x^2-10=0
We multiply all the terms by the denominator
12x+(-2x)-10*8x^2=0
Wy multiply elements
-80x^2+12x+(-2x)=0
We get rid of parentheses
-80x^2+12x-2x=0
We add all the numbers together, and all the variables
-80x^2+10x=0
a = -80; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-80)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-80}=\frac{-20}{-160} =1/8 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-80}=\frac{0}{-160} =0 $

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