3(x+3)(-2x+1)/2=0.5

Solution for 3(x+3)(-2x+1)/2=0.5 equation:

3(x+3)(-2x+1)/2=0.5

We move all terms to the left:

3(x+3)(-2x+1)/2-(0.5)=0

We add all the numbers together, and all the variables

3(x+3)(-2x+1)/2-0.5=0

We multiply parentheses ..

3(-2x^2+x-6x+3)/2-0.5=0

We multiply all the terms by the denominator


3(-2x^2+x-6x+3)-(0.5)*2=0

We add all the numbers together, and all the variables

3(-2x^2+x-6x+3)-1=0

We multiply parentheses

-6x^2+3x-18x+9-1=0

We add all the numbers together, and all the variables

-6x^2-15x+8=0

a = -6; b = -15; c = +8;
Δ = b2-4ac
Δ = -152-4·(-6)·8
Δ = 417
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{-(-15)-\sqrt{417}}{2*-6}=\frac{15-\sqrt{417}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{417}}{2*-6}=\frac{15+\sqrt{417}}{-12}
$