8/x=1/2x+45

Solution for 8/x=1/2x+45 equation:

8/x=1/2x+45

We move all terms to the left:

8/x-(1/2x+45)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+45)!=0

x∈R


We get rid of parentheses

8/x-1/2x-45=0

We calculate fractions


16x/2x^2+(-x)/2x^2-45=0

We add all the numbers together, and all the variables

16x/2x^2+(-1x)/2x^2-45=0

We multiply all the terms by the denominator


16x+(-1x)-45*2x^2=0

Wy multiply elements

-90x^2+16x+(-1x)=0

We get rid of parentheses

-90x^2+16x-1x=0

We add all the numbers together, and all the variables

-90x^2+15x=0

a = -90; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-90)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-90}=\frac{-30}{-180}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-90}=\frac{0}{-180}
=0
$