21/2x+2/3x=15/6

Solution for 21/2x+2/3x=15/6 equation:

21/2x+2/3x=15/6

We move all terms to the left:

21/2x+2/3x-(15/6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

21/2x+2/3x-(+15/6)=0

We get rid of parentheses

21/2x+2/3x-15/6=0

We calculate fractions


(-270x^2)/216x^2+2268x/216x^2+144x/216x^2=0

We multiply all the terms by the denominator


(-270x^2)+2268x+144x=0

We add all the numbers together, and all the variables

(-270x^2)+2412x=0

We get rid of parentheses

-270x^2+2412x=0

a = -270; b = 2412; c = 0;
Δ = b2-4ac
Δ = 24122-4·(-270)·0
Δ = 5817744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5817744}=2412$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2412)-2412}{2*-270}=\frac{-4824}{-540}
=8+14/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2412)+2412}{2*-270}=\frac{0}{-540}
=0
$