0=-3/2*x+1

Solution for 0=-3/2*x+1 equation:

0=-3/2*x+1

We move all terms to the left:

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


Domain of the equation: 2*x+1)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/2*x-1=0

We multiply all the terms by the denominator


-1*2*x+3=0

Wy multiply elements

-2x*x+3=0

Wy multiply elements

-2x^2+3=0

a = -2; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-2)·3
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-2}=\frac{0-2\sqrt{6}}{-4}
=-\frac{2\sqrt{6}}{-4}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-2}=\frac{0+2\sqrt{6}}{-4}
=\frac{2\sqrt{6}}{-4}
=\frac{\sqrt{6}}{-2}
$