2/5x+5=7/15x+15

Solution for 2/5x+5=7/15x+15 equation:

2/5x+5=7/15x+15

We move all terms to the left:

2/5x+5-(7/15x+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

2/5x-7/15x-15+5=0

We calculate fractions


30x/75x^2+(-35x)/75x^2-15+5=0

We add all the numbers together, and all the variables

30x/75x^2+(-35x)/75x^2-10=0

We multiply all the terms by the denominator


30x+(-35x)-10*75x^2=0

Wy multiply elements

-750x^2+30x+(-35x)=0

We get rid of parentheses

-750x^2+30x-35x=0

We add all the numbers together, and all the variables

-750x^2-5x=0

a = -750; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-750)·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*-750}=\frac{0}{-1500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-750}=\frac{10}{-1500}
=-1/150
$