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

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

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


Domain of the equation: (4x^2-9)!=0

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

4x^2!=9

x^2!=9/4

x^2!=√2+1/4

x!=1.41421356237

x∈R


We multiply all the terms by the denominator


(x^2-25)=0

We get rid of parentheses

x^2-25=0

a = 1; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·1·(-25)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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