(8x-3)(5x+9)=0

Solution for (8x-3)(5x+9)=0 equation:

(8x-3)(5x+9)=0

We multiply parentheses ..

(+40x^2+72x-15x-27)=0

We get rid of parentheses

40x^2+72x-15x-27=0

We add all the numbers together, and all the variables

40x^2+57x-27=0

a = 40; b = 57; c = -27;
Δ = b2-4ac
Δ = 572-4·40·(-27)
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-87}{2*40}=\frac{-144}{80}
=-1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+87}{2*40}=\frac{30}{80}
=3/8
$