2/3x+3=1/5x+10

Solution for 2/3x+3=1/5x+10 equation:

2/3x+3=1/5x+10

We move all terms to the left:

2/3x+3-(1/5x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

2/3x-1/5x-10+3=0

We calculate fractions


10x/15x^2+(-3x)/15x^2-10+3=0

We add all the numbers together, and all the variables

10x/15x^2+(-3x)/15x^2-7=0

We multiply all the terms by the denominator


10x+(-3x)-7*15x^2=0

Wy multiply elements

-105x^2+10x+(-3x)=0

We get rid of parentheses

-105x^2+10x-3x=0

We add all the numbers together, and all the variables

-105x^2+7x=0

a = -105; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-105)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-105}=\frac{-14}{-210}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-105}=\frac{0}{-210}
=0
$