7n^2-8=69

Solution for 7n^2-8=69 equation:

7n^2-8=69

We move all terms to the left:

7n^2-8-(69)=0

We add all the numbers together, and all the variables

7n^2-77=0

a = 7; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·7·(-77)
Δ = 2156
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:

$\sqrt{\Delta}=\sqrt{2156}=\sqrt{196*11}=\sqrt{196}*\sqrt{11}=14\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{11}}{2*7}=\frac{0-14\sqrt{11}}{14}
=-\frac{14\sqrt{11}}{14}
=-\sqrt{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{11}}{2*7}=\frac{0+14\sqrt{11}}{14}
=\frac{14\sqrt{11}}{14}
=\sqrt{11}
$