10=19x/(x^2-9)

Solution for 10=19x/(x^2-9) equation:

10=19x/(x^2-9)

We move all terms to the left:

10-(19x/(x^2-9))=0


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

x∈R


We multiply all the terms by the denominator


-(19x+10*(x^2-9))=0


We calculate terms in parentheses: -(19x+10*(x^2-9)), so:

19x+10*(x^2-9)

We multiply parentheses

10x^2+19x-90

Back to the equation:

-(10x^2+19x-90)


We get rid of parentheses

-10x^2-19x+90=0

a = -10; b = -19; c = +90;
Δ = b2-4ac
Δ = -192-4·(-10)·90
Δ = 3961
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{-(-19)-\sqrt{3961}}{2*-10}=\frac{19-\sqrt{3961}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{3961}}{2*-10}=\frac{19+\sqrt{3961}}{-20}
$