2x(2x-1)=420

Solution for 2x(2x-1)=420 equation:

2x(2x-1)=420

We move all terms to the left:

2x(2x-1)-(420)=0

We multiply parentheses

4x^2-2x-420=0

a = 4; b = -2; c = -420;
Δ = b2-4ac
Δ = -22-4·4·(-420)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-82}{2*4}=\frac{-80}{8}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+82}{2*4}=\frac{84}{8}
=10+1/2
$