7n2=9-10n

Solution for 7n2=9-10n equation:

7n^2=9-10n

We move all terms to the left:

7n^2-(9-10n)=0

We add all the numbers together, and all the variables

7n^2-(-10n+9)=0

We get rid of parentheses

7n^2+10n-9=0

a = 7; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·7·(-9)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{22}}{2*7}=\frac{-10-4\sqrt{22}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{22}}{2*7}=\frac{-10+4\sqrt{22}}{14}
$