(3x)(4x+1)-3(x+1)=45

Solution for (3x)(4x+1)-3(x+1)=45 equation:

(3x)(4x+1)-3(x+1)=45

We move all terms to the left:

(3x)(4x+1)-3(x+1)-(45)=0

We multiply parentheses

12x^2+3x-3x-3-45=0

We add all the numbers together, and all the variables

12x^2-48=0

a = 12; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·12·(-48)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*12}=\frac{-48}{24}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*12}=\frac{48}{24}
=2
$