(x^2-8x+16)/(x^2)=30

Solution for (x^2-8x+16)/(x^2)=30 equation:

(x^2-8x+16)/(x^2)=30

We move all terms to the left:

(x^2-8x+16)/(x^2)-(30)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


(x^2-8x+16)-30*x^2=0

We add all the numbers together, and all the variables

-30x^2+(x^2-8x+16)=0

We get rid of parentheses

-30x^2+x^2-8x+16=0

We add all the numbers together, and all the variables

-29x^2-8x+16=0

a = -29; b = -8; c = +16;
Δ = b2-4ac
Δ = -82-4·(-29)·16
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{30}}{2*-29}=\frac{8-8\sqrt{30}}{-58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{30}}{2*-29}=\frac{8+8\sqrt{30}}{-58}
$