(3x+1)x=8

Solution for (3x+1)x=8 equation:

(3x+1)x=8

We move all terms to the left:

(3x+1)x-(8)=0

We multiply parentheses

3x^2+x-8=0

a = 3; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·3·(-8)
Δ = 97
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{-(1)-\sqrt{97}}{2*3}=\frac{-1-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*3}=\frac{-1+\sqrt{97}}{6}
$