-.032x2+46x-3000=0

Solution for -.032x2+46x-3000=0 equation:

-.032x^2+46x-3000=0

We add all the numbers together, and all the variables

-0.032x^2+46x-3000=0

a = -0.032; b = 46; c = -3000;
Δ = b2-4ac
Δ = 462-4·(-0.032)·(-3000)
Δ = 1732
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:

$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{433}}{2*-0.032}=\frac{-46-2\sqrt{433}}{-0.064}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{433}}{2*-0.032}=\frac{-46+2\sqrt{433}}{-0.064}
$