(4x^2-25)/(x^2+9)=0

Solution for (4x^2-25)/(x^2+9)=0 equation:

(4x^2-25)/(x^2+9)=0


Domain of the equation: (x^2+9)!=0

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

x^2!=-9

x^2!=-9/

x^2!=√-1/0

x!=NAN

x∈R


We multiply all the terms by the denominator


(4x^2-25)=0

We get rid of parentheses

4x^2-25=0

a = 4; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·4·(-25)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*4}=\frac{20}{8}
=2+1/2
$