0=x^2-175x+40,000

Solution for 0=x^2-175x+40,000 equation:

0=x^2-175x+40.000

We move all terms to the left:

0-(x^2-175x+40.000)=0

We add all the numbers together, and all the variables

-(x^2-175x+40.000)=0

We get rid of parentheses

-x^2+175x-40.000=0

We add all the numbers together, and all the variables

-1x^2+175x-40=0

a = -1; b = 175; c = -40;
Δ = b2-4ac
Δ = 1752-4·(-1)·(-40)
Δ = 30465
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:

$\sqrt{\Delta}=\sqrt{30465}=\sqrt{9*3385}=\sqrt{9}*\sqrt{3385}=3\sqrt{3385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(175)-3\sqrt{3385}}{2*-1}=\frac{-175-3\sqrt{3385}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(175)+3\sqrt{3385}}{2*-1}=\frac{-175+3\sqrt{3385}}{-2}
$