-.1x2+100x-1690=0

Solution for -.1x2+100x-1690=0 equation:

-.1x^2+100x-1690=0

We add all the numbers together, and all the variables

-0.1x^2+100x-1690=0

a = -0.1; b = 100; c = -1690;
Δ = b2-4ac
Δ = 1002-4·(-0.1)·(-1690)
Δ = 9324
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:

$\sqrt{\Delta}=\sqrt{9324}=\sqrt{36*259}=\sqrt{36}*\sqrt{259}=6\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-6\sqrt{259}}{2*-0.1}=\frac{-100-6\sqrt{259}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+6\sqrt{259}}{2*-0.1}=\frac{-100+6\sqrt{259}}{-0.2}
$