420=3x^2+8x

Solution for 420=3x^2+8x equation:

420=3x^2+8x

We move all terms to the left:

420-(3x^2+8x)=0

We get rid of parentheses

-3x^2-8x+420=0

a = -3; b = -8; c = +420;
Δ = b2-4ac
Δ = -82-4·(-3)·420
Δ = 5104
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:

$\sqrt{\Delta}=\sqrt{5104}=\sqrt{16*319}=\sqrt{16}*\sqrt{319}=4\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{319}}{2*-3}=\frac{8-4\sqrt{319}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{319}}{2*-3}=\frac{8+4\sqrt{319}}{-6}
$