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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+36x^2+8x-45x-10)=0

We get rid of parentheses

36x^2+8x-45x-10=0

We add all the numbers together, and all the variables

36x^2-37x-10=0

a = 36; b = -37; c = -10;
Δ = b2-4ac
Δ = -372-4·36·(-10)
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*36}=\frac{-16}{72}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+53}{2*36}=\frac{90}{72}
=1+1/4
$