(5n+11)(n-3)=0

Solution for (5n+11)(n-3)=0 equation:

(5n+11)(n-3)=0

We multiply parentheses ..

(+5n^2-15n+11n-33)=0

We get rid of parentheses

5n^2-15n+11n-33=0

We add all the numbers together, and all the variables

5n^2-4n-33=0

a = 5; b = -4; c = -33;
Δ = b2-4ac
Δ = -42-4·5·(-33)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-26}{2*5}=\frac{-22}{10}
=-2+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+26}{2*5}=\frac{30}{10}
=3
$