8.x-3=20/x

Solution for 8.x-3=20/x equation:

8.x-3=20/x

We move all terms to the left:

8.x-3-(20/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

8.x-(+20/x)-3=0

We get rid of parentheses

8.x-20/x-3=0

We multiply all the terms by the denominator


(8.x)*x-3*x-20=0

We add all the numbers together, and all the variables

(+8.x)*x-3*x-20=0

We add all the numbers together, and all the variables

-3x+(+8.x)*x-20=0

We multiply parentheses

8x^2-3x-20=0

a = 8; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·8·(-20)
Δ = 649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{649}}{2*8}=\frac{3-\sqrt{649}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{649}}{2*8}=\frac{3+\sqrt{649}}{16}
$