x+1/8x=180

Solution for x+1/8x=180 equation:

x+1/8x=180

We move all terms to the left:

x+1/8x-(180)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


x*8x-180*8x+1=0

Wy multiply elements

8x^2-1440x+1=0

a = 8; b = -1440; c = +1;
Δ = b2-4ac
Δ = -14402-4·8·1
Δ = 2073568
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:

$\sqrt{\Delta}=\sqrt{2073568}=\sqrt{16*129598}=\sqrt{16}*\sqrt{129598}=4\sqrt{129598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-4\sqrt{129598}}{2*8}=\frac{1440-4\sqrt{129598}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+4\sqrt{129598}}{2*8}=\frac{1440+4\sqrt{129598}}{16}
$