X(3x+13)=2

Solution for X(3x+13)=2 equation:

X(3X+13)=2

We move all terms to the left:

X(3X+13)-(2)=0

We multiply parentheses

3X^2+13X-2=0

a = 3; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·3·(-2)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{193}}{2*3}=\frac{-13-\sqrt{193}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{193}}{2*3}=\frac{-13+\sqrt{193}}{6}
$