(x+4)(320/x)=188

Solution for (x+4)(320/x)=188 equation:

(x+4)(320/x)=188

We move all terms to the left:

(x+4)(320/x)-(188)=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+4)(+320/x)-188=0

We multiply parentheses ..

(+320x^2+1280x)-188=0

We get rid of parentheses

320x^2+1280x-188=0

a = 320; b = 1280; c = -188;
Δ = b2-4ac
Δ = 12802-4·320·(-188)
Δ = 1879040
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:

$\sqrt{\Delta}=\sqrt{1879040}=\sqrt{1024*1835}=\sqrt{1024}*\sqrt{1835}=32\sqrt{1835}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1280)-32\sqrt{1835}}{2*320}=\frac{-1280-32\sqrt{1835}}{640}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1280)+32\sqrt{1835}}{2*320}=\frac{-1280+32\sqrt{1835}}{640}
$