10n^2-7=243

Solution for 10n^2-7=243 equation:

10n^2-7=243

We move all terms to the left:

10n^2-7-(243)=0

We add all the numbers together, and all the variables

10n^2-250=0

a = 10; b = 0; c = -250;
Δ = b2-4ac
Δ = 02-4·10·(-250)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*10}=\frac{-100}{20}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*10}=\frac{100}{20}
=5
$