(4x-1)(6x+9)=147

Solution for (4x-1)(6x+9)=147 equation:

(4x-1)(6x+9)=147

We move all terms to the left:

(4x-1)(6x+9)-(147)=0

We multiply parentheses ..

(+24x^2+36x-6x-9)-147=0

We get rid of parentheses

24x^2+36x-6x-9-147=0

We add all the numbers together, and all the variables

24x^2+30x-156=0

a = 24; b = 30; c = -156;
Δ = b2-4ac
Δ = 302-4·24·(-156)
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-126}{2*24}=\frac{-156}{48}
=-3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+126}{2*24}=\frac{96}{48}
=2
$