400=-4x^2+100x-180

Solution for 400=-4x^2+100x-180 equation:

400=-4x^2+100x-180

We move all terms to the left:

400-(-4x^2+100x-180)=0

We get rid of parentheses

4x^2-100x+180+400=0

We add all the numbers together, and all the variables

4x^2-100x+580=0

a = 4; b = -100; c = +580;
Δ = b2-4ac
Δ = -1002-4·4·580
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-12\sqrt{5}}{2*4}=\frac{100-12\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+12\sqrt{5}}{2*4}=\frac{100+12\sqrt{5}}{8}
$