1/8x+x=72

Solution for 1/8x+x=72 equation:

1/8x+x=72

We move all terms to the left:

1/8x+x-(72)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/8x-72=0

We multiply all the terms by the denominator


x*8x-72*8x+1=0

Wy multiply elements

8x^2-576x+1=0

a = 8; b = -576; c = +1;
Δ = b2-4ac
Δ = -5762-4·8·1
Δ = 331744
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:

$\sqrt{\Delta}=\sqrt{331744}=\sqrt{16*20734}=\sqrt{16}*\sqrt{20734}=4\sqrt{20734}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-4\sqrt{20734}}{2*8}=\frac{576-4\sqrt{20734}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+4\sqrt{20734}}{2*8}=\frac{576+4\sqrt{20734}}{16}
$