3x(4x+9)=12x+27

Solution for 3x(4x+9)=12x+27 equation:

3x(4x+9)=12x+27

We move all terms to the left:

3x(4x+9)-(12x+27)=0

We multiply parentheses

12x^2+27x-(12x+27)=0

We get rid of parentheses

12x^2+27x-12x-27=0

We add all the numbers together, and all the variables

12x^2+15x-27=0

a = 12; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·12·(-27)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-39}{2*12}=\frac{-54}{24}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+39}{2*12}=\frac{24}{24}
=1
$