(3x+1)(x+1)=45

Solution for (3x+1)(x+1)=45 equation:

(3x+1)(x+1)=45

We move all terms to the left:

(3x+1)(x+1)-(45)=0

We multiply parentheses ..

(+3x^2+3x+x+1)-45=0

We get rid of parentheses

3x^2+3x+x+1-45=0

We add all the numbers together, and all the variables

3x^2+4x-44=0

a = 3; b = 4; c = -44;
Δ = b2-4ac
Δ = 42-4·3·(-44)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{34}}{2*3}=\frac{-4-4\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{34}}{2*3}=\frac{-4+4\sqrt{34}}{6}
$