120+4x/x=8x

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Solution for 120+4x/x=8x equation:



120+4x/x=8x
We move all terms to the left:
120+4x/x-(8x)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
-8x+4x/x+120=0
We multiply all the terms by the denominator
-8x*x+4x+120*x=0
We add all the numbers together, and all the variables
124x-8x*x=0
Wy multiply elements
-8x^2+124x=0
a = -8; b = 124; c = 0;
Δ = b2-4ac
Δ = 1242-4·(-8)·0
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-124}{2*-8}=\frac{-248}{-16} =15+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+124}{2*-8}=\frac{0}{-16} =0 $

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