X^2-1=4-x^/4

Solution for X^2-1=4-x^/4 equation:

X^2-1=4-X^/4

We move all terms to the left:

X^2-1-(4-X^/4)=0

We get rid of parentheses

X^2+X^/4-4-1=0

We multiply all the terms by the denominator


X^2*4+X^-4*4-1*4=0

We add all the numbers together, and all the variables

X^2*4+X-20=0

Wy multiply elements

4X^2+X-20=0

a = 4; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·4·(-20)
Δ = 321
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{-(1)-\sqrt{321}}{2*4}=\frac{-1-\sqrt{321}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{321}}{2*4}=\frac{-1+\sqrt{321}}{8}
$