40=-425x^2+45000x-650000

Solution for 40=-425x^2+45000x-650000 equation:

40=-425x^2+45000x-650000

We move all terms to the left:

40-(-425x^2+45000x-650000)=0

We get rid of parentheses

425x^2-45000x+650000+40=0

We add all the numbers together, and all the variables

425x^2-45000x+650040=0

a = 425; b = -45000; c = +650040;
Δ = b2-4ac
Δ = -450002-4·425·650040
Δ = 919932000
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:

$\sqrt{\Delta}=\sqrt{919932000}=\sqrt{400*2299830}=\sqrt{400}*\sqrt{2299830}=20\sqrt{2299830}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45000)-20\sqrt{2299830}}{2*425}=\frac{45000-20\sqrt{2299830}}{850}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45000)+20\sqrt{2299830}}{2*425}=\frac{45000+20\sqrt{2299830}}{850}
$