4x2-178x-420=0

Solution for 4x2-178x-420=0 equation:

4x^2-178x-420=0

a = 4; b = -178; c = -420;
Δ = b2-4ac
Δ = -1782-4·4·(-420)
Δ = 38404
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:

$\sqrt{\Delta}=\sqrt{38404}=\sqrt{4*9601}=\sqrt{4}*\sqrt{9601}=2\sqrt{9601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-2\sqrt{9601}}{2*4}=\frac{178-2\sqrt{9601}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+2\sqrt{9601}}{2*4}=\frac{178+2\sqrt{9601}}{8}
$