9/25x=5/3x^-2

Solution for 9/25x=5/3x^-2 equation:

9/25x=5/3x^-2

We move all terms to the left:

9/25x-(5/3x^-2)=0


Domain of the equation: 25x!=0

x!=0/25

x!=0

x∈R



Domain of the equation: 3x^-2)!=0

x∈R


We get rid of parentheses

9/25x-5/3x^+2=0

We calculate fractions


27x/75x^2+(-125x)/75x^2+2=0

We multiply all the terms by the denominator


27x+(-125x)+2*75x^2=0

Wy multiply elements

150x^2+27x+(-125x)=0

We get rid of parentheses

150x^2+27x-125x=0

We add all the numbers together, and all the variables

150x^2-98x=0

a = 150; b = -98; c = 0;
Δ = b2-4ac
Δ = -982-4·150·0
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-98}{2*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+98}{2*150}=\frac{196}{300}
=49/75
$