8/x=x-63

Solution for 8/x=x-63 equation:

8/x=x-63

We move all terms to the left:

8/x-(x-63)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8/x-x+63=0

We multiply all the terms by the denominator


-x*x+63*x+8=0

We add all the numbers together, and all the variables

63x-x*x+8=0

Wy multiply elements

-1x^2+63x+8=0

a = -1; b = 63; c = +8;
Δ = b2-4ac
Δ = 632-4·(-1)·8
Δ = 4001
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{-(63)-\sqrt{4001}}{2*-1}=\frac{-63-\sqrt{4001}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{4001}}{2*-1}=\frac{-63+\sqrt{4001}}{-2}
$