(2x-5)(9x+12)=0

Solution for (2x-5)(9x+12)=0 equation:

(2x-5)(9x+12)=0

We multiply parentheses ..

(+18x^2+24x-45x-60)=0

We get rid of parentheses

18x^2+24x-45x-60=0

We add all the numbers together, and all the variables

18x^2-21x-60=0

a = 18; b = -21; c = -60;
Δ = b2-4ac
Δ = -212-4·18·(-60)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-69}{2*18}=\frac{-48}{36}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+69}{2*18}=\frac{90}{36}
=2+1/2
$