(3x+1)x=52

Solution for (3x+1)x=52 equation:

(3x+1)x=52

We move all terms to the left:

(3x+1)x-(52)=0

We multiply parentheses

3x^2+x-52=0

a = 3; b = 1; c = -52;
Δ = b2-4ac
Δ = 12-4·3·(-52)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-25}{2*3}=\frac{-26}{6}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+25}{2*3}=\frac{24}{6}
=4
$