64/8x+120=16x

Solution for 64/8x+120=16x equation:

64/8x+120=16x

We move all terms to the left:

64/8x+120-(16x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-16x+64/8x+120=0

We multiply all the terms by the denominator


-16x*8x+120*8x+64=0

Wy multiply elements

-128x^2+960x+64=0

a = -128; b = 960; c = +64;
Δ = b2-4ac
Δ = 9602-4·(-128)·64
Δ = 954368
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{954368}=\sqrt{4096*233}=\sqrt{4096}*\sqrt{233}=64\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(960)-64\sqrt{233}}{2*-128}=\frac{-960-64\sqrt{233}}{-256}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(960)+64\sqrt{233}}{2*-128}=\frac{-960+64\sqrt{233}}{-256}
$