400=120+x+8/x

Solution for 400=120+x+8/x equation:

400=120+x+8/x

We move all terms to the left:

400-(120+x+8/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(x+8/x+120)+400=0

We get rid of parentheses

-x-8/x-120+400=0

We multiply all the terms by the denominator


-x*x-120*x+400*x-8=0

We add all the numbers together, and all the variables

280x-x*x-8=0

Wy multiply elements

-1x^2+280x-8=0

a = -1; b = 280; c = -8;
Δ = b2-4ac
Δ = 2802-4·(-1)·(-8)
Δ = 78368
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:

$\sqrt{\Delta}=\sqrt{78368}=\sqrt{16*4898}=\sqrt{16}*\sqrt{4898}=4\sqrt{4898}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-4\sqrt{4898}}{2*-1}=\frac{-280-4\sqrt{4898}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+4\sqrt{4898}}{2*-1}=\frac{-280+4\sqrt{4898}}{-2}
$