(X-2)/(x^2-3x-10)=10

Solution for (X-2)/(x^2-3x-10)=10 equation:

(X-2)/(X^2-3X-10)=10

We move all terms to the left:

(X-2)/(X^2-3X-10)-(10)=0


Domain of the equation: (X^2-3X-10)!=0

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

X^2-3X!=10

X∈R


We multiply all the terms by the denominator


(X-2)-10*(X^2-3X-10)=0

We multiply parentheses

-10X^2+(X-2)+30X+100=0

We get rid of parentheses

-10X^2+X+30X-2+100=0

We add all the numbers together, and all the variables

-10X^2+31X+98=0

a = -10; b = 31; c = +98;
Δ = b2-4ac
Δ = 312-4·(-10)·98
Δ = 4881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{4881}}{2*-10}=\frac{-31-\sqrt{4881}}{-20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{4881}}{2*-10}=\frac{-31+\sqrt{4881}}{-20}
$