(2x-5)(8x+9)=0

Solution for (2x-5)(8x+9)=0 equation:

(2x-5)(8x+9)=0

We multiply parentheses ..

(+16x^2+18x-40x-45)=0

We get rid of parentheses

16x^2+18x-40x-45=0

We add all the numbers together, and all the variables

16x^2-22x-45=0

a = 16; b = -22; c = -45;
Δ = b2-4ac
Δ = -222-4·16·(-45)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-58}{2*16}=\frac{-36}{32}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+58}{2*16}=\frac{80}{32}
=2+1/2
$