-2/3x+3=1/5x+11

Solution for -2/3x+3=1/5x+11 equation:

-2/3x+3=1/5x+11

We move all terms to the left:

-2/3x+3-(1/5x+11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+11)!=0

x∈R


We get rid of parentheses

-2/3x-1/5x-11+3=0

We calculate fractions


(-10x)/15x^2+(-3x)/15x^2-11+3=0

We add all the numbers together, and all the variables

(-10x)/15x^2+(-3x)/15x^2-8=0

We multiply all the terms by the denominator


(-10x)+(-3x)-8*15x^2=0

Wy multiply elements

-120x^2+(-10x)+(-3x)=0

We get rid of parentheses

-120x^2-10x-3x=0

We add all the numbers together, and all the variables

-120x^2-13x=0

a = -120; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-120)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-120}=\frac{26}{-240}
=-13/120
$