5/2x+17=-2/3x-21

Solution for 5/2x+17=-2/3x-21 equation:

5/2x+17=-2/3x-21

We move all terms to the left:

5/2x+17-(-2/3x-21)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-21)!=0

x∈R


We get rid of parentheses

5/2x+2/3x+21+17=0

We calculate fractions


15x/6x^2+4x/6x^2+21+17=0

We add all the numbers together, and all the variables

15x/6x^2+4x/6x^2+38=0

We multiply all the terms by the denominator


15x+4x+38*6x^2=0

We add all the numbers together, and all the variables

19x+38*6x^2=0

Wy multiply elements

228x^2+19x=0

a = 228; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·228·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*228}=\frac{-38}{456}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*228}=\frac{0}{456}
=0
$