x-3/2xx-1=22.5

Solution for x-3/2xx-1=22.5 equation:

x-3/2xx-1=22.5

We move all terms to the left:

x-3/2xx-1-(22.5)=0


Domain of the equation: 2xx!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/2xx-23.5=0

We multiply all the terms by the denominator


x*2xx-(23.5)*2xx-3=0

We multiply parentheses

x*2xx-47x-3=0

Wy multiply elements

2x^2-47x-3=0

a = 2; b = -47; c = -3;
Δ = b2-4ac
Δ = -472-4·2·(-3)
Δ = 2233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{2233}}{2*2}=\frac{47-\sqrt{2233}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2233}}{2*2}=\frac{47+\sqrt{2233}}{4}
$