-5x-17=2/3x-4

Solution for -5x-17=2/3x-4 equation:

-5x-17=2/3x-4

We move all terms to the left:

-5x-17-(2/3x-4)=0


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

-5x-2/3x+4-17=0

We multiply all the terms by the denominator


-5x*3x+4*3x-17*3x-2=0

Wy multiply elements

-15x^2+12x-51x-2=0

We add all the numbers together, and all the variables

-15x^2-39x-2=0

a = -15; b = -39; c = -2;
Δ = b2-4ac
Δ = -392-4·(-15)·(-2)
Δ = 1401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1401}}{2*-15}=\frac{39-\sqrt{1401}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1401}}{2*-15}=\frac{39+\sqrt{1401}}{-30}
$