4x^2-176x+420=0

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

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}
$