16=(25x)/(x^2-6)

Solution for 16=(25x)/(x^2-6) equation:

16=(25x)/(x^2-6)

We move all terms to the left:

16-((25x)/(x^2-6))=0


Domain of the equation: (x^2-6))!=0

x∈R


We multiply all the terms by the denominator


-(25x+16*(x^2-6))=0


We calculate terms in parentheses: -(25x+16*(x^2-6)), so:

25x+16*(x^2-6)

We multiply parentheses

16x^2+25x-96

Back to the equation:

-(16x^2+25x-96)


We get rid of parentheses

-16x^2-25x+96=0

a = -16; b = -25; c = +96;
Δ = b2-4ac
Δ = -252-4·(-16)·96
Δ = 6769
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{-(-25)-\sqrt{6769}}{2*-16}=\frac{25-\sqrt{6769}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{6769}}{2*-16}=\frac{25+\sqrt{6769}}{-32}
$