3x(4x+9)+7x=27

Solution for 3x(4x+9)+7x=27 equation:

3x(4x+9)+7x=27

We move all terms to the left:

3x(4x+9)+7x-(27)=0

We add all the numbers together, and all the variables

7x+3x(4x+9)-27=0

We multiply parentheses

12x^2+7x+27x-27=0

We add all the numbers together, and all the variables

12x^2+34x-27=0

a = 12; b = 34; c = -27;
Δ = b2-4ac
Δ = 342-4·12·(-27)
Δ = 2452
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:

$\sqrt{\Delta}=\sqrt{2452}=\sqrt{4*613}=\sqrt{4}*\sqrt{613}=2\sqrt{613}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{613}}{2*12}=\frac{-34-2\sqrt{613}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{613}}{2*12}=\frac{-34+2\sqrt{613}}{24}
$