(3x+8)x(x)=420

Solution for (3x+8)x(x)=420 equation:

(3x+8)x(x)=420

We move all terms to the left:

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

We multiply 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}
$