7/3x+15=7/15x+3

Solution for 7/3x+15=7/15x+3 equation:

7/3x+15=7/15x+3

We move all terms to the left:

7/3x+15-(7/15x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 15x+3)!=0

x∈R


We get rid of parentheses

7/3x-7/15x-3+15=0

We calculate fractions


105x/45x^2+(-21x)/45x^2-3+15=0

We add all the numbers together, and all the variables

105x/45x^2+(-21x)/45x^2+12=0

We multiply all the terms by the denominator


105x+(-21x)+12*45x^2=0

Wy multiply elements

540x^2+105x+(-21x)=0

We get rid of parentheses

540x^2+105x-21x=0

We add all the numbers together, and all the variables

540x^2+84x=0

a = 540; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·540·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*540}=\frac{-168}{1080}
=-7/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*540}=\frac{0}{1080}
=0
$