2(x-1)x+1/2=32

Solution for 2(x-1)x+1/2=32 equation:

2(x-1)x+1/2=32

We move all terms to the left:

2(x-1)x+1/2-(32)=0

determiningTheFunctionDomain
2(x-1)x-32+1/2=0

We multiply parentheses

2x^2-2x-32+1/2=0

We multiply all the terms by the denominator


2x^2*2-2x*2+1-32*2=0

We add all the numbers together, and all the variables

2x^2*2-2x*2-63=0

Wy multiply elements

4x^2-4x-63=0

a = 4; b = -4; c = -63;
Δ = b2-4ac
Δ = -42-4·4·(-63)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*4}=\frac{36}{8}
=4+1/2
$