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

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

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

We multiply parentheses ..

(+40x^2-72x+25x-45)=0

We get rid of parentheses

40x^2-72x+25x-45=0

We add all the numbers together, and all the variables

40x^2-47x-45=0

a = 40; b = -47; c = -45;
Δ = b2-4ac
Δ = -472-4·40·(-45)
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-97}{2*40}=\frac{-50}{80}
=-5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+97}{2*40}=\frac{144}{80}
=1+4/5
$