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

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

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

We multiply parentheses ..

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

We get rid of parentheses

28x^2+63x-20x-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{-126}{56}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+83}{2*28}=\frac{40}{56}
=5/7
$