2/3x+1=17/15x+3

Solution for 2/3x+1=17/15x+3 equation:

2/3x+1=17/15x+3

We move all terms to the left:

2/3x+1-(17/15x+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

2/3x-17/15x-3+1=0

We calculate fractions


30x/45x^2+(-51x)/45x^2-3+1=0

We add all the numbers together, and all the variables

30x/45x^2+(-51x)/45x^2-2=0

We multiply all the terms by the denominator


30x+(-51x)-2*45x^2=0

Wy multiply elements

-90x^2+30x+(-51x)=0

We get rid of parentheses

-90x^2+30x-51x=0

We add all the numbers together, and all the variables

-90x^2-21x=0

a = -90; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-90)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-90}=\frac{42}{-180}
=-7/30
$