(5x^2-30)/(x^2+6)=0

Solution for (5x^2-30)/(x^2+6)=0 equation:

(5x^2-30)/(x^2+6)=0


Domain of the equation: (x^2+6)!=0

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

x^2!=-6

x^2!=-6/

x^2!=√-1/0

x!=NAN

x∈R


We multiply all the terms by the denominator


(5x^2-30)=0

We get rid of parentheses

5x^2-30=0

a = 5; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·5·(-30)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*5}=\frac{0-10\sqrt{6}}{10}
=-\frac{10\sqrt{6}}{10}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*5}=\frac{0+10\sqrt{6}}{10}
=\frac{10\sqrt{6}}{10}
=\sqrt{6}
$