x(3/2*x)=121.5

Solution for x(3/2*x)=121.5 equation:

x(3/2x)=121.5

We move all terms to the left:

x(3/2x)-(121.5)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+3/2x)-(121.5)=0

We add all the numbers together, and all the variables

x(+3/2x)-121.5=0

We multiply parentheses

3x^2-121.5=0

a = 3; b = 0; c = -121.5;
Δ = b2-4ac
Δ = 02-4·3·(-121.5)
Δ = 1458
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:

$\sqrt{\Delta}=\sqrt{1458}=\sqrt{729*2}=\sqrt{729}*\sqrt{2}=27\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-27\sqrt{2}}{2*3}=\frac{0-27\sqrt{2}}{6}
=-\frac{27\sqrt{2}}{6}
=-\frac{9\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+27\sqrt{2}}{2*3}=\frac{0+27\sqrt{2}}{6}
=\frac{27\sqrt{2}}{6}
=\frac{9\sqrt{2}}{2}
$