(4x^2-12x-16)/(4x^2+28x+24)=0

Solution for (4x^2-12x-16)/(4x^2+28x+24)=0 equation:

(4x^2-12x-16)/(4x^2+28x+24)=0


Domain of the equation: (4x^2+28x+24)!=0

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

4x^2+28x!=-24

x∈R


We multiply all the terms by the denominator


(4x^2-12x-16)=0

We get rid of parentheses

4x^2-12x-16=0

a = 4; b = -12; c = -16;
Δ = b2-4ac
Δ = -122-4·4·(-16)
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{-(-12)-20}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*4}=\frac{32}{8}
=4
$