4n^2+10=130

Solution for 4n^2+10=130 equation:

4n^2+10=130

We move all terms to the left:

4n^2+10-(130)=0

We add all the numbers together, and all the variables

4n^2-120=0

a = 4; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·4·(-120)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*4}=\frac{0-8\sqrt{30}}{8}
=-\frac{8\sqrt{30}}{8}
=-\sqrt{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*4}=\frac{0+8\sqrt{30}}{8}
=\frac{8\sqrt{30}}{8}
=\sqrt{30}
$