4n^2-2n-11=-7n-5

Solution for 4n^2-2n-11=-7n-5 equation:

4n^2-2n-11=-7n-5

We move all terms to the left:

4n^2-2n-11-(-7n-5)=0

We get rid of parentheses

4n^2-2n+7n+5-11=0

We add all the numbers together, and all the variables

4n^2+5n-6=0

a = 4; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·4·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*4}=\frac{-16}{8}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*4}=\frac{6}{8}
=3/4
$