4x/6x+4=x/25

Solution for 4x/6x+4=x/25 equation:

4x/6x+4=x/25

We move all terms to the left:

4x/6x+4-(x/25)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

4x/6x-(+x/25)+4=0

We get rid of parentheses

4x/6x-x/25+4=0

We calculate fractions


(-6x^2)/150x+100x/150x+4=0

We multiply all the terms by the denominator


(-6x^2)+100x+4*150x=0

Wy multiply elements

(-6x^2)+100x+600x=0

We get rid of parentheses

-6x^2+100x+600x=0

We add all the numbers together, and all the variables

-6x^2+700x=0

a = -6; b = 700; c = 0;
Δ = b2-4ac
Δ = 7002-4·(-6)·0
Δ = 490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{490000}=700$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-700}{2*-6}=\frac{-1400}{-12}
=116+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+700}{2*-6}=\frac{0}{-12}
=0
$