(7n-2)(5n-4=0)

Solution for (7n-2)(5n-4=0) equation:

(7n-2)(5n-4=0)

We move all terms to the left:

(7n-2)(5n-4-(0))=0

We add all the numbers together, and all the variables

(7n-2)(5n-4)=0

We multiply parentheses ..

(+35n^2-28n-10n+8)=0

We get rid of parentheses

35n^2-28n-10n+8=0

We add all the numbers together, and all the variables

35n^2-38n+8=0

a = 35; b = -38; c = +8;
Δ = b2-4ac
Δ = -382-4·35·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-18}{2*35}=\frac{20}{70}
=2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+18}{2*35}=\frac{56}{70}
=4/5
$