(5x-9)(8x+1)=0

Solution for (5x-9)(8x+1)=0 equation:

(5x-9)(8x+1)=0

We multiply parentheses ..

(+40x^2+5x-72x-9)=0

We get rid of parentheses

40x^2+5x-72x-9=0

We add all the numbers together, and all the variables

40x^2-67x-9=0

a = 40; b = -67; c = -9;
Δ = b2-4ac
Δ = -672-4·40·(-9)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-77}{2*40}=\frac{-10}{80}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+77}{2*40}=\frac{144}{80}
=1+4/5
$