420-178x+4x^2=0

Solution for 420-178x+4x^2=0 equation:

420-178x+4x^2=0

a = 4; b = -178; c = +420;
Δ = b2-4ac
Δ = -1782-4·4·420
Δ = 24964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24964}=158$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-158}{2*4}=\frac{20}{8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+158}{2*4}=\frac{336}{8}
=42
$