(3x+2)(x)=170

Solution for (3x+2)(x)=170 equation:

(3x+2)(x)=170

We move all terms to the left:

(3x+2)(x)-(170)=0

We multiply parentheses

3x^2+2x-170=0

a = 3; b = 2; c = -170;
Δ = b2-4ac
Δ = 22-4·3·(-170)
Δ = 2044
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:

$\sqrt{\Delta}=\sqrt{2044}=\sqrt{4*511}=\sqrt{4}*\sqrt{511}=2\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{511}}{2*3}=\frac{-2-2\sqrt{511}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{511}}{2*3}=\frac{-2+2\sqrt{511}}{6}
$