30(x^2+1/x^2)-77(x-1/x)-12=0

Solution for 30(x^2+1/x^2)-77(x-1/x)-12=0 equation:

30(x^2+1/x^2)-77(x-1/x)-12=0


Domain of the equation: x^2)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

30(x^2+1/x^2)-77(+x-1/x)-12=0

We multiply parentheses

30x^2+30x-77x+77x-12=0

We add all the numbers together, and all the variables

30x^2+30x-12=0

a = 30; b = 30; c = -12;
Δ = b2-4ac
Δ = 302-4·30·(-12)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{65}}{2*30}=\frac{-30-6\sqrt{65}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{65}}{2*30}=\frac{-30+6\sqrt{65}}{60}
$