45=3x(3x+12)

Solution for 45=3x(3x+12) equation:

45=3x(3x+12)

We move all terms to the left:

45-(3x(3x+12))=0


We calculate terms in parentheses: -(3x(3x+12)), so:

3x(3x+12)

We multiply parentheses

9x^2+36x

Back to the equation:

-(9x^2+36x)


We get rid of parentheses

-9x^2-36x+45=0

a = -9; b = -36; c = +45;
Δ = b2-4ac
Δ = -362-4·(-9)·45
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-54}{2*-9}=\frac{-18}{-18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+54}{2*-9}=\frac{90}{-18}
=-5
$