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

Solution for x(-2x+3)=1/2 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

-2x^2+3x-1/2=0

We multiply all the terms by the denominator


-2x^2*2+3x*2-1=0

Wy multiply elements

-4x^2+6x-1=0

a = -4; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-4)·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*-4}=\frac{-6-2\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*-4}=\frac{-6+2\sqrt{5}}{-8}
$