120+4x/x=8x

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
$