1/25x+2=1/30x+4

Solution for 1/25x+2=1/30x+4 equation:

1/25x+2=1/30x+4

We move all terms to the left:

1/25x+2-(1/30x+4)=0


Domain of the equation: 25x!=0

x!=0/25

x!=0

x∈R



Domain of the equation: 30x+4)!=0

x∈R


We get rid of parentheses

1/25x-1/30x-4+2=0

We calculate fractions


30x/750x^2+(-25x)/750x^2-4+2=0

We add all the numbers together, and all the variables

30x/750x^2+(-25x)/750x^2-2=0

We multiply all the terms by the denominator


30x+(-25x)-2*750x^2=0

Wy multiply elements

-1500x^2+30x+(-25x)=0

We get rid of parentheses

-1500x^2+30x-25x=0

We add all the numbers together, and all the variables

-1500x^2+5x=0

a = -1500; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1500)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-1500}=\frac{-10}{-3000}
=1/300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1500}=\frac{0}{-3000}
=0
$