(-3/(x^2+9x-10))-(12/(x^2-49))=0

Solution for (-3/(x^2+9x-10))-(12/(x^2-49))=0 equation:

(-3/(x^2+9x-10))-(12/(x^2-49))=0


Domain of the equation: (x^2+9x-10))!=0

x∈R



Domain of the equation: (x^2-49))!=0

x∈R


We calculate fractions


(-3x^2+147)/((x^2+9x-10))*x^2+(-12x^2-108x+120)/((x^2+9x-10))*x^2=0

We multiply all the terms by the denominator


(-3x^2+147)+(-12x^2-108x+120)=0

We get rid of parentheses

-3x^2-12x^2-108x+147+120=0

We add all the numbers together, and all the variables

-15x^2-108x+267=0

a = -15; b = -108; c = +267;
Δ = b2-4ac
Δ = -1082-4·(-15)·267
Δ = 27684
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:

$\sqrt{\Delta}=\sqrt{27684}=\sqrt{36*769}=\sqrt{36}*\sqrt{769}=6\sqrt{769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-6\sqrt{769}}{2*-15}=\frac{108-6\sqrt{769}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+6\sqrt{769}}{2*-15}=\frac{108+6\sqrt{769}}{-30}
$