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

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

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

We multiply parentheses ..

(+35x^2-28x+45x-36)=0

We get rid of parentheses

35x^2-28x+45x-36=0

We add all the numbers together, and all the variables

35x^2+17x-36=0

a = 35; b = 17; c = -36;
Δ = b2-4ac
Δ = 172-4·35·(-36)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-73}{2*35}=\frac{-90}{70}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+73}{2*35}=\frac{56}{70}
=4/5
$