/3x+9=5x+21

Solution for /3x+9=5x+21 equation:

/3x+9=5x+21

We move all terms to the left:

/3x+9-(5x+21)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

/3x-5x-21+9=0

We multiply all the terms by the denominator


-5x*3x-21*3x+9*3x+=0

We add all the numbers together, and all the variables

-5x*3x-21*3x+9*3x=0

Wy multiply elements

-15x^2-63x+27x=0

We add all the numbers together, and all the variables

-15x^2-36x=0

a = -15; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-15)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-15}=\frac{72}{-30}
=-2+2/5
$