-3000+85x-0.2x^2=0

Solution for -3000+85x-0.2x^2=0 equation:

-3000+85x-0.2x^2=0

a = -0.2; b = 85; c = -3000;
Δ = b2-4ac
Δ = 852-4·(-0.2)·(-3000)
Δ = 4825
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:

$\sqrt{\Delta}=\sqrt{4825}=\sqrt{25*193}=\sqrt{25}*\sqrt{193}=5\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-5\sqrt{193}}{2*-0.2}=\frac{-85-5\sqrt{193}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+5\sqrt{193}}{2*-0.2}=\frac{-85+5\sqrt{193}}{-0.4}
$