(3/2x)(x)=75

Solution for (3/2x)(x)=75 equation:

(3/2x)(x)=75

We move all terms to the left:

(3/2x)(x)-(75)=0


Domain of the equation: 2x)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/2x)x-75=0

We multiply parentheses

3x^2-75=0

a = 3; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·3·(-75)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*3}=\frac{30}{6}
=5
$