.25x^2-10x+800=900

Solution for .25x^2-10x+800=900 equation:

.25x^2-10x+800=900

We move all terms to the left:

.25x^2-10x+800-(900)=0

We add all the numbers together, and all the variables

.25x^2-10x-100=0

a = .25; b = -10; c = -100;
Δ = b2-4ac
Δ = -102-4·.25·(-100)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{2}}{2*.25}=\frac{10-10\sqrt{2}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{2}}{2*.25}=\frac{10+10\sqrt{2}}{0.5}
$