10n^2+6=21n+7

Solution for 10n^2+6=21n+7 equation:

10n^2+6=21n+7

We move all terms to the left:

10n^2+6-(21n+7)=0

We get rid of parentheses

10n^2-21n-7+6=0

We add all the numbers together, and all the variables

10n^2-21n-1=0

a = 10; b = -21; c = -1;
Δ = b2-4ac
Δ = -212-4·10·(-1)
Δ = 481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{481}}{2*10}=\frac{21-\sqrt{481}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{481}}{2*10}=\frac{21+\sqrt{481}}{20}
$