(3x-1)(x)=420

Solution for (3x-1)(x)=420 equation:

(3x-1)(x)=420

We move all terms to the left:

(3x-1)(x)-(420)=0

We multiply parentheses

3x^2-1x-420=0

a = 3; b = -1; c = -420;
Δ = b2-4ac
Δ = -12-4·3·(-420)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-71}{2*3}=\frac{-70}{6}
=-11+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+71}{2*3}=\frac{72}{6}
=12
$