7n2=5n+6

Solution for 7n2=5n+6 equation:

7n^2=5n+6

We move all terms to the left:

7n^2-(5n+6)=0

We get rid of parentheses

7n^2-5n-6=0

a = 7; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·7·(-6)
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{-(-5)-\sqrt{193}}{2*7}=\frac{5-\sqrt{193}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*7}=\frac{5+\sqrt{193}}{14}
$