x(3x+1)=352

Solution for x(3x+1)=352 equation:

x(3x+1)=352

We move all terms to the left:

x(3x+1)-(352)=0

We multiply parentheses

3x^2+x-352=0

a = 3; b = 1; c = -352;
Δ = b2-4ac
Δ = 12-4·3·(-352)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-65}{2*3}=\frac{-66}{6}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+65}{2*3}=\frac{64}{6}
=10+2/3
$