(n-6)(4n-7)=0

Solution for (n-6)(4n-7)=0 equation:

(n-6)(4n-7)=0

We multiply parentheses ..

(+4n^2-7n-24n+42)=0

We get rid of parentheses

4n^2-7n-24n+42=0

We add all the numbers together, and all the variables

4n^2-31n+42=0

a = 4; b = -31; c = +42;
Δ = b2-4ac
Δ = -312-4·4·42
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-17}{2*4}=\frac{14}{8}
=1+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+17}{2*4}=\frac{48}{8}
=6
$