9/2x=51/10x-30

Solution for 9/2x=51/10x-30 equation:

9/2x=51/10x-30

We move all terms to the left:

9/2x-(51/10x-30)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x-30)!=0

x∈R


We get rid of parentheses

9/2x-51/10x+30=0

We calculate fractions


90x/20x^2+(-102x)/20x^2+30=0

We multiply all the terms by the denominator


90x+(-102x)+30*20x^2=0

Wy multiply elements

600x^2+90x+(-102x)=0

We get rid of parentheses

600x^2+90x-102x=0

We add all the numbers together, and all the variables

600x^2-12x=0

a = 600; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·600·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*600}=\frac{0}{1200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*600}=\frac{24}{1200}
=1/50
$