(4x+9)(8x-3)=0

Solution for (4x+9)(8x-3)=0 equation:

(4x+9)(8x-3)=0

We multiply parentheses ..

(+32x^2-12x+72x-27)=0

We get rid of parentheses

32x^2-12x+72x-27=0

We add all the numbers together, and all the variables

32x^2+60x-27=0

a = 32; b = 60; c = -27;
Δ = b2-4ac
Δ = 602-4·32·(-27)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-84}{2*32}=\frac{-144}{64}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+84}{2*32}=\frac{24}{64}
=3/8
$