9n2=4+7n

Solution for 9n2=4+7n equation:

9n^2=4+7n

We move all terms to the left:

9n^2-(4+7n)=0

We add all the numbers together, and all the variables

9n^2-(7n+4)=0

We get rid of parentheses

9n^2-7n-4=0

a = 9; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·9·(-4)
Δ = 193
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{-(-7)-\sqrt{193}}{2*9}=\frac{7-\sqrt{193}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{193}}{2*9}=\frac{7+\sqrt{193}}{18}
$