(x+1)(3x+1)=54

Solution for (x+1)(3x+1)=54 equation:

(x+1)(3x+1)=54

We move all terms to the left:

(x+1)(3x+1)-(54)=0

We multiply parentheses ..

(+3x^2+x+3x+1)-54=0

We get rid of parentheses

3x^2+x+3x+1-54=0

We add all the numbers together, and all the variables

3x^2+4x-53=0

a = 3; b = 4; c = -53;
Δ = b2-4ac
Δ = 42-4·3·(-53)
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{163}}{2*3}=\frac{-4-2\sqrt{163}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{163}}{2*3}=\frac{-4+2\sqrt{163}}{6}
$