(5n+9)(7n-5)=0

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

(5n+9)(7n-5)=0

We multiply parentheses ..

(+35n^2-25n+63n-45)=0

We get rid of parentheses

35n^2-25n+63n-45=0

We add all the numbers together, and all the variables

35n^2+38n-45=0

a = 35; b = 38; c = -45;
Δ = b2-4ac
Δ = 382-4·35·(-45)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-88}{2*35}=\frac{-126}{70}
=-1+4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+88}{2*35}=\frac{50}{70}
=5/7
$