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

Solution for (x+6)(4x-9)=0 equation:

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

We multiply parentheses ..

(+4x^2-9x+24x-54)=0

We get rid of parentheses

4x^2-9x+24x-54=0

We add all the numbers together, and all the variables

4x^2+15x-54=0

a = 4; b = 15; c = -54;
Δ = b2-4ac
Δ = 152-4·4·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-33}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+33}{2*4}=\frac{18}{8}
=2+1/4
$