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

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

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

We multiply parentheses ..

(+2x^2-18x+5x-45)=0

We get rid of parentheses

2x^2-18x+5x-45=0

We add all the numbers together, and all the variables

2x^2-13x-45=0

a = 2; b = -13; c = -45;
Δ = b2-4ac
Δ = -132-4·2·(-45)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*2}=\frac{36}{4}
=9
$