10n^2-10=-21n

Solution for 10n^2-10=-21n equation:

10n^2-10=-21n

We move all terms to the left:

10n^2-10-(-21n)=0

We get rid of parentheses

10n^2+21n-10=0

a = 10; b = 21; c = -10;
Δ = b2-4ac
Δ = 212-4·10·(-10)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-29}{2*10}=\frac{-50}{20}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+29}{2*10}=\frac{8}{20}
=2/5
$