(2x+5)(9x-4)=0

Solution for (2x+5)(9x-4)=0 equation:

(2x+5)(9x-4)=0

We multiply parentheses ..

(+18x^2-8x+45x-20)=0

We get rid of parentheses

18x^2-8x+45x-20=0

We add all the numbers together, and all the variables

18x^2+37x-20=0

a = 18; b = 37; c = -20;
Δ = b2-4ac
Δ = 372-4·18·(-20)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-53}{2*18}=\frac{-90}{36}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+53}{2*18}=\frac{16}{36}
=4/9
$