1/5x-2/3x=-7/25

Solution for 1/5x-2/3x=-7/25 equation:

1/5x-2/3x=-7/25

We move all terms to the left:

1/5x-2/3x-(-7/25)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/5x-2/3x+7/25=0

We calculate fractions


315x^2/750x^2+150x/750x^2+(-500x)/750x^2=0

We multiply all the terms by the denominator


315x^2+150x+(-500x)=0

We get rid of parentheses

315x^2+150x-500x=0

We add all the numbers together, and all the variables

315x^2-350x=0

a = 315; b = -350; c = 0;
Δ = b2-4ac
Δ = -3502-4·315·0
Δ = 122500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{122500}=350$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-350}{2*315}=\frac{0}{630}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+350}{2*315}=\frac{700}{630}
=1+1/9
$