49n^2-8=49

Solution for 49n^2-8=49 equation:

49n^2-8=49

We move all terms to the left:

49n^2-8-(49)=0

We add all the numbers together, and all the variables

49n^2-57=0

a = 49; b = 0; c = -57;
Δ = b2-4ac
Δ = 02-4·49·(-57)
Δ = 11172
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:

$\sqrt{\Delta}=\sqrt{11172}=\sqrt{196*57}=\sqrt{196}*\sqrt{57}=14\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{57}}{2*49}=\frac{0-14\sqrt{57}}{98}
=-\frac{14\sqrt{57}}{98}
=-\frac{\sqrt{57}}{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{57}}{2*49}=\frac{0+14\sqrt{57}}{98}
=\frac{14\sqrt{57}}{98}
=\frac{\sqrt{57}}{7}
$