4x^2-100x+600=416

Solution for 4x^2-100x+600=416 equation:

4x^2-100x+600=416

We move all terms to the left:

4x^2-100x+600-(416)=0

We add all the numbers together, and all the variables

4x^2-100x+184=0

a = 4; b = -100; c = +184;
Δ = b2-4ac
Δ = -1002-4·4·184
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-84}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+84}{2*4}=\frac{184}{8}
=23
$