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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4n^2-17n-42=0

a = 4; b = -17; c = -42;
Δ = b2-4ac
Δ = -172-4·4·(-42)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-31}{2*4}=\frac{-14}{8}
=-1+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+31}{2*4}=\frac{48}{8}
=6
$