x+1/8x+1/8x+x=180

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

x+1/8x+1/8x+x=180

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/8x+1/8x-180=0

We multiply all the terms by the denominator


2x*8x-180*8x+1+1=0

We add all the numbers together, and all the variables

2x*8x-180*8x+2=0

Wy multiply elements

16x^2-1440x+2=0

a = 16; b = -1440; c = +2;
Δ = b2-4ac
Δ = -14402-4·16·2
Δ = 2073472
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:

$\sqrt{\Delta}=\sqrt{2073472}=\sqrt{64*32398}=\sqrt{64}*\sqrt{32398}=8\sqrt{32398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-8\sqrt{32398}}{2*16}=\frac{1440-8\sqrt{32398}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+8\sqrt{32398}}{2*16}=\frac{1440+8\sqrt{32398}}{32}
$