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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2+31x-72=0

a = 5; b = 31; c = -72;
Δ = b2-4ac
Δ = 312-4·5·(-72)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-49}{2*5}=\frac{-80}{10}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+49}{2*5}=\frac{18}{10}
=1+4/5
$