0=4x^2-176x+420

Solution for 0=4x^2-176x+420 equation:

0=4x^2-176x+420

We move all terms to the left:

0-(4x^2-176x+420)=0

We add all the numbers together, and all the variables

-(4x^2-176x+420)=0

We get rid of parentheses

-4x^2+176x-420=0

a = -4; b = 176; c = -420;
Δ = b2-4ac
Δ = 1762-4·(-4)·(-420)
Δ = 24256
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:

$\sqrt{\Delta}=\sqrt{24256}=\sqrt{64*379}=\sqrt{64}*\sqrt{379}=8\sqrt{379}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-8\sqrt{379}}{2*-4}=\frac{-176-8\sqrt{379}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+8\sqrt{379}}{2*-4}=\frac{-176+8\sqrt{379}}{-8}
$