(4n+3)(n-7)=0

Solution for (4n+3)(n-7)=0 equation:

(4n+3)(n-7)=0

We multiply parentheses ..

(+4n^2-28n+3n-21)=0

We get rid of parentheses

4n^2-28n+3n-21=0

We add all the numbers together, and all the variables

4n^2-25n-21=0

a = 4; b = -25; c = -21;
Δ = b2-4ac
Δ = -252-4·4·(-21)
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{-(-25)-31}{2*4}=\frac{-6}{8}
=-3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+31}{2*4}=\frac{56}{8}
=7
$