(X^2-2x-48)/(x^2+15x+54)=0

Solution for (X^2-2x-48)/(x^2+15x+54)=0 equation:

(X^2-2X-48)/(X^2+15X+54)=0


Domain of the equation: (X^2+15X+54)!=0

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

X^2+15X!=-54

X∈R


We multiply all the terms by the denominator


(X^2-2X-48)=0

We get rid of parentheses

X^2-2X-48=0

a = 1; b = -2; c = -48;
Δ = b2-4ac
Δ = -22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*1}=\frac{16}{2}
=8
$