7/5x+3=1+8/15x

Solution for 7/5x+3=1+8/15x equation:

7/5x+3=1+8/15x

We move all terms to the left:

7/5x+3-(1+8/15x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/5x-(8/15x+1)+3=0

We get rid of parentheses

7/5x-8/15x-1+3=0

We calculate fractions


105x/75x^2+(-40x)/75x^2-1+3=0

We add all the numbers together, and all the variables

105x/75x^2+(-40x)/75x^2+2=0

We multiply all the terms by the denominator


105x+(-40x)+2*75x^2=0

Wy multiply elements

150x^2+105x+(-40x)=0

We get rid of parentheses

150x^2+105x-40x=0

We add all the numbers together, and all the variables

150x^2+65x=0

a = 150; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·150·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*150}=\frac{-130}{300}
=-13/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*150}=\frac{0}{300}
=0
$