1/5x+1/3=10/15x+15

Solution for 1/5x+1/3=10/15x+15 equation:

1/5x+1/3=10/15x+15

We move all terms to the left:

1/5x+1/3-(10/15x+15)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/5x-10/15x-15+1/3=0

We calculate fractions


75x^2/675x^2+135x/675x^2+(-450x)/675x^2-15=0

We multiply all the terms by the denominator


75x^2+135x+(-450x)-15*675x^2=0

Wy multiply elements

75x^2-10125x^2+135x+(-450x)=0

We get rid of parentheses

75x^2-10125x^2+135x-450x=0

We add all the numbers together, and all the variables

-10050x^2-315x=0

a = -10050; b = -315; c = 0;
Δ = b2-4ac
Δ = -3152-4·(-10050)·0
Δ = 99225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{99225}=315$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-315)-315}{2*-10050}=\frac{0}{-20100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-315)+315}{2*-10050}=\frac{630}{-20100}
=-21/670
$