x=360/x+4

Solution for x=360/x+4 equation:

x=360/x+4

We move all terms to the left:

x-(360/x+4)=0


Domain of the equation: x+4)!=0

x∈R


We get rid of parentheses

x-360/x-4=0

We multiply all the terms by the denominator


x*x-4*x-360=0

We add all the numbers together, and all the variables

-4x+x*x-360=0

Wy multiply elements

x^2-4x-360=0

a = 1; b = -4; c = -360;
Δ = b2-4ac
Δ = -42-4·1·(-360)
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{91}}{2*1}=\frac{4-4\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{91}}{2*1}=\frac{4+4\sqrt{91}}{2}
$