(x)(3x+2)=390

Solution for (x)(3x+2)=390 equation:

(x)(3x+2)=390

We move all terms to the left:

(x)(3x+2)-(390)=0

We multiply parentheses

3x^2+2x-390=0

a = 3; b = 2; c = -390;
Δ = b2-4ac
Δ = 22-4·3·(-390)
Δ = 4684
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:

$\sqrt{\Delta}=\sqrt{4684}=\sqrt{4*1171}=\sqrt{4}*\sqrt{1171}=2\sqrt{1171}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1171}}{2*3}=\frac{-2-2\sqrt{1171}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1171}}{2*3}=\frac{-2+2\sqrt{1171}}{6}
$