-.2x^2+90x-1500=0

Solution for -.2x^2+90x-1500=0 equation:

-.2x^2+90x-1500=0

We add all the numbers together, and all the variables

-0.2x^2+90x-1500=0

a = -0.2; b = 90; c = -1500;
Δ = b2-4ac
Δ = 902-4·(-0.2)·(-1500)
Δ = 6900
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:

$\sqrt{\Delta}=\sqrt{6900}=\sqrt{100*69}=\sqrt{100}*\sqrt{69}=10\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{69}}{2*-0.2}=\frac{-90-10\sqrt{69}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{69}}{2*-0.2}=\frac{-90+10\sqrt{69}}{-0.4}
$