8x-0,25x^2=-12

Solution for 8x-0,25x^2=-12 equation:

8x-0.25x^2=-12

We move all terms to the left:

8x-0.25x^2-(-12)=0

We add all the numbers together, and all the variables

-0.25x^2+8x+12=0

a = -0.25; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-0.25)·12
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*-0.25}=\frac{-8-2\sqrt{19}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*-0.25}=\frac{-8+2\sqrt{19}}{-0.5}
$