10n^2-24=20n+9

Solution for 10n^2-24=20n+9 equation:

10n^2-24=20n+9

We move all terms to the left:

10n^2-24-(20n+9)=0

We get rid of parentheses

10n^2-20n-9-24=0

We add all the numbers together, and all the variables

10n^2-20n-33=0

a = 10; b = -20; c = -33;
Δ = b2-4ac
Δ = -202-4·10·(-33)
Δ = 1720
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:

$\sqrt{\Delta}=\sqrt{1720}=\sqrt{4*430}=\sqrt{4}*\sqrt{430}=2\sqrt{430}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{430}}{2*10}=\frac{20-2\sqrt{430}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{430}}{2*10}=\frac{20+2\sqrt{430}}{20}
$