3x+(3/2)x=27

Solution for 3x+(3/2)x=27 equation:

3x+(3/2)x=27

We move all terms to the left:

3x+(3/2)x-(27)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x+(+3/2)x-27=0

We multiply parentheses

3x^2+3x-27=0

a = 3; b = 3; c = -27;
Δ = b2-4ac
Δ = 32-4·3·(-27)
Δ = 333
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{37}}{2*3}=\frac{-3-3\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{37}}{2*3}=\frac{-3+3\sqrt{37}}{6}
$