-x^2+10x-8.5=0

Solution for -x^2+10x-8.5=0 equation:

-x^2+10x-8.5=0

We add all the numbers together, and all the variables

-1x^2+10x-8.5=0

a = -1; b = 10; c = -8.5;
Δ = b2-4ac
Δ = 102-4·(-1)·(-8.5)
Δ = 66
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-\sqrt{66}}{2*-1}=\frac{-10-\sqrt{66}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+\sqrt{66}}{2*-1}=\frac{-10+\sqrt{66}}{-2}
$