8x=180/x

Solution for 8x=180/x equation:

8x=180/x

We move all terms to the left:

8x-(180/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+180/x)=0

We get rid of parentheses

8x-180/x=0

We multiply all the terms by the denominator


8x*x-180=0

Wy multiply elements

8x^2-180=0

a = 8; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·8·(-180)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{10}}{2*8}=\frac{0-24\sqrt{10}}{16}
=-\frac{24\sqrt{10}}{16}
=-\frac{3\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{10}}{2*8}=\frac{0+24\sqrt{10}}{16}
=\frac{24\sqrt{10}}{16}
=\frac{3\sqrt{10}}{2}
$