-0.5x(12x-8)+2=-24

Solution for -0.5x(12x-8)+2=-24 equation:

-0.5x(12x-8)+2=-24

We move all terms to the left:

-0.5x(12x-8)+2-(-24)=0

We add all the numbers together, and all the variables

-0.5x(12x-8)+26=0

We multiply parentheses

-0x^2-0x+26=0

We add all the numbers together, and all the variables

-1x^2-1x+26=0

a = -1; b = -1; c = +26;
Δ = b2-4ac
Δ = -12-4·(-1)·26
Δ = 105
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{-(-1)-\sqrt{105}}{2*-1}=\frac{1-\sqrt{105}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{105}}{2*-1}=\frac{1+\sqrt{105}}{-2}
$