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

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

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

We multiply parentheses ..

(+10x^2-18x+45x-81)=0

We get rid of parentheses

10x^2-18x+45x-81=0

We add all the numbers together, and all the variables

10x^2+27x-81=0

a = 10; b = 27; c = -81;
Δ = b2-4ac
Δ = 272-4·10·(-81)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-63}{2*10}=\frac{-90}{20}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+63}{2*10}=\frac{36}{20}
=1+4/5
$