7n^2-152=11n+4

Solution for 7n^2-152=11n+4 equation:

7n^2-152=11n+4

We move all terms to the left:

7n^2-152-(11n+4)=0

We get rid of parentheses

7n^2-11n-4-152=0

We add all the numbers together, and all the variables

7n^2-11n-156=0

a = 7; b = -11; c = -156;
Δ = b2-4ac
Δ = -112-4·7·(-156)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-67}{2*7}=\frac{-56}{14}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+67}{2*7}=\frac{78}{14}
=5+4/7
$