6x/(20-5x2)=6

Solution for 6x/(20-5x2)=6 equation:

6x/(20-5x^2)=6

We move all terms to the left:

6x/(20-5x^2)-(6)=0


Domain of the equation: (20-5x^2)!=0

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

-5x^2!=-20

x^2!=-20/-5

x^2!=√+4

x!=2

x∈R


We multiply all the terms by the denominator


-6*(20-5x^2)+6x=0

We multiply parentheses

30x^2+6x-120=0

a = 30; b = 6; c = -120;
Δ = b2-4ac
Δ = 62-4·30·(-120)
Δ = 14436
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:

$\sqrt{\Delta}=\sqrt{14436}=\sqrt{36*401}=\sqrt{36}*\sqrt{401}=6\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{401}}{2*30}=\frac{-6-6\sqrt{401}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{401}}{2*30}=\frac{-6+6\sqrt{401}}{60}
$