(-5x^2+6)/(X^2-1)=0

Solution for (-5x^2+6)/(X^2-1)=0 equation:

(-5x^2+6)/(x^2-1)=0


Domain of the equation: (x^2-1)!=0

We move all terms containing x to the left, all other terms to the right

x^2!=1

x^2!=1/

x^2!=√1/

x!=1

x∈R


We multiply all the terms by the denominator


(-5x^2+6)=0

We get rid of parentheses

-5x^2+6=0

a = -5; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-5)·6
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-5}=\frac{0-2\sqrt{30}}{-10}
=-\frac{2\sqrt{30}}{-10}
=-\frac{\sqrt{30}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-5}=\frac{0+2\sqrt{30}}{-10}
=\frac{2\sqrt{30}}{-10}
=\frac{\sqrt{30}}{-5}
$