(4x-9)(7x+5)=0

Solution for (4x-9)(7x+5)=0 equation:

(4x-9)(7x+5)=0

We multiply parentheses ..

(+28x^2+20x-63x-45)=0

We get rid of parentheses

28x^2+20x-63x-45=0

We add all the numbers together, and all the variables

28x^2-43x-45=0

a = 28; b = -43; c = -45;
Δ = b2-4ac
Δ = -432-4·28·(-45)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-83}{2*28}=\frac{-40}{56}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+83}{2*28}=\frac{126}{56}
=2+1/4
$