7n^2-7=112

Solution for 7n^2-7=112 equation:

7n^2-7=112

We move all terms to the left:

7n^2-7-(112)=0

We add all the numbers together, and all the variables

7n^2-119=0

a = 7; b = 0; c = -119;
Δ = b2-4ac
Δ = 02-4·7·(-119)
Δ = 3332
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:

$\sqrt{\Delta}=\sqrt{3332}=\sqrt{196*17}=\sqrt{196}*\sqrt{17}=14\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{17}}{2*7}=\frac{0-14\sqrt{17}}{14}
=-\frac{14\sqrt{17}}{14}
=-\sqrt{17}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{17}}{2*7}=\frac{0+14\sqrt{17}}{14}
=\frac{14\sqrt{17}}{14}
=\sqrt{17}
$