-8/15x-11=4/9x+17

Solution for -8/15x-11=4/9x+17 equation:

-8/15x-11=4/9x+17

We move all terms to the left:

-8/15x-11-(4/9x+17)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 9x+17)!=0

x∈R


We get rid of parentheses

-8/15x-4/9x-17-11=0

We calculate fractions


(-72x)/135x^2+(-60x)/135x^2-17-11=0

We add all the numbers together, and all the variables

(-72x)/135x^2+(-60x)/135x^2-28=0

We multiply all the terms by the denominator


(-72x)+(-60x)-28*135x^2=0

Wy multiply elements

-3780x^2+(-72x)+(-60x)=0

We get rid of parentheses

-3780x^2-72x-60x=0

We add all the numbers together, and all the variables

-3780x^2-132x=0

a = -3780; b = -132; c = 0;
Δ = b2-4ac
Δ = -1322-4·(-3780)·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-132}{2*-3780}=\frac{0}{-7560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+132}{2*-3780}=\frac{264}{-7560}
=-11/315
$