1/4x+1/5=25/6x+15

Solution for 1/4x+1/5=25/6x+15 equation:

1/4x+1/5=25/6x+15

We move all terms to the left:

1/4x+1/5-(25/6x+15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+15)!=0

x∈R


We get rid of parentheses

1/4x-25/6x-15+1/5=0

We calculate fractions


144x^2/600x^2+150x/600x^2+(-2500x)/600x^2-15=0

We multiply all the terms by the denominator


144x^2+150x+(-2500x)-15*600x^2=0

Wy multiply elements

144x^2-9000x^2+150x+(-2500x)=0

We get rid of parentheses

144x^2-9000x^2+150x-2500x=0

We add all the numbers together, and all the variables

-8856x^2-2350x=0

a = -8856; b = -2350; c = 0;
Δ = b2-4ac
Δ = -23502-4·(-8856)·0
Δ = 5522500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5522500}=2350$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2350)-2350}{2*-8856}=\frac{0}{-17712}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2350)+2350}{2*-8856}=\frac{4700}{-17712}
=-1175/4428
$