7n^2-5=611

Solution for 7n^2-5=611 equation:

7n^2-5=611

We move all terms to the left:

7n^2-5-(611)=0

We add all the numbers together, and all the variables

7n^2-616=0

a = 7; b = 0; c = -616;
Δ = b2-4ac
Δ = 02-4·7·(-616)
Δ = 17248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17248}=\sqrt{784*22}=\sqrt{784}*\sqrt{22}=28\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{22}}{2*7}=\frac{0-28\sqrt{22}}{14}
=-\frac{28\sqrt{22}}{14}
=-2\sqrt{22}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{22}}{2*7}=\frac{0+28\sqrt{22}}{14}
=\frac{28\sqrt{22}}{14}
=2\sqrt{22}
$