x+(1/2)x+(2/3)x=30

Solution for x+(1/2)x+(2/3)x=30 equation:

x+(1/2)x+(2/3)x=30

We move all terms to the left:

x+(1/2)x+(2/3)x-(30)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+1/2)x+(+2/3)x-30=0

We multiply parentheses

x^2+2x^2+x-30=0

We add all the numbers together, and all the variables

3x^2+x-30=0

a = 3; b = 1; c = -30;
Δ = b2-4ac
Δ = 12-4·3·(-30)
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{-(1)-19}{2*3}=\frac{-20}{6}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*3}=\frac{18}{6}
=3
$