(x*x)2/x=1089

Solution for (x*x)2/x=1089 equation:

(x*x)2/x=1089

We move all terms to the left:

(x*x)2/x-(1089)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(+x*x)2/x-1089=0

We multiply all the terms by the denominator


(+x*x)2-1089*x=0

We add all the numbers together, and all the variables

-1089x+(+x*x)2=0

We multiply parentheses

2x^2-1089x=0

a = 2; b = -1089; c = 0;
Δ = b2-4ac
Δ = -10892-4·2·0
Δ = 1185921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1185921}=1089$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1089)-1089}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1089)+1089}{2*2}=\frac{2178}{4}
=544+1/2
$