2n^2=11n+15

Solution for 2n^2=11n+15 equation:

2n^2=11n+15

We move all terms to the left:

2n^2-(11n+15)=0

We get rid of parentheses

2n^2-11n-15=0

a = 2; b = -11; c = -15;
Δ = b2-4ac
Δ = -112-4·2·(-15)
Δ = 241
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{-(-11)-\sqrt{241}}{2*2}=\frac{11-\sqrt{241}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{241}}{2*2}=\frac{11+\sqrt{241}}{4}
$