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

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

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

We multiply parentheses ..

(+10x^2+4x-45x-18)=0

We get rid of parentheses

10x^2+4x-45x-18=0

We add all the numbers together, and all the variables

10x^2-41x-18=0

a = 10; b = -41; c = -18;
Δ = b2-4ac
Δ = -412-4·10·(-18)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-49}{2*10}=\frac{-8}{20}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+49}{2*10}=\frac{90}{20}
=4+1/2
$