-.1x^2+112x-3000=0

Solution for -.1x^2+112x-3000=0 equation:

-.1x^2+112x-3000=0

We add all the numbers together, and all the variables

-0.1x^2+112x-3000=0

a = -0.1; b = 112; c = -3000;
Δ = b2-4ac
Δ = 1122-4·(-0.1)·(-3000)
Δ = 11344
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:

$\sqrt{\Delta}=\sqrt{11344}=\sqrt{16*709}=\sqrt{16}*\sqrt{709}=4\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{709}}{2*-0.1}=\frac{-112-4\sqrt{709}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{709}}{2*-0.1}=\frac{-112+4\sqrt{709}}{-0.2}
$