52=(3x+1)(x)

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

52=(3x+1)(x)

We move all terms to the left:

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


We calculate terms in parentheses: -((3x+1)x), so:

(3x+1)x

We multiply parentheses

3x^2+x

Back to the equation:

-(3x^2+x)


We get rid of parentheses

-3x^2-x+52=0

We add all the numbers together, and all the variables

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