30/5x-7x^2/5x=x/10

Solution for 30/5x-7x^2/5x=x/10 equation:

30/5x-7x^2/5x=x/10

We move all terms to the left:

30/5x-7x^2/5x-(x/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-7x^2/5x+30/5x-(+x/10)=0

We get rid of parentheses

-7x^2/5x+30/5x-x/10=0

We calculate fractions


(-7x^2+300)/50x+(-5x^2)/50x=0

We multiply all the terms by the denominator


(-7x^2+300)+(-5x^2)=0

We get rid of parentheses

-7x^2-5x^2+300=0

We add all the numbers together, and all the variables

-12x^2+300=0

a = -12; b = 0; c = +300;
Δ = b2-4ac
Δ = 02-4·(-12)·300
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*-12}=\frac{-120}{-24}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*-12}=\frac{120}{-24}
=-5
$