5n^2=22n+15

Solution for 5n^2=22n+15 equation:

5n^2=22n+15

We move all terms to the left:

5n^2-(22n+15)=0

We get rid of parentheses

5n^2-22n-15=0

a = 5; b = -22; c = -15;
Δ = b2-4ac
Δ = -222-4·5·(-15)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-28}{2*5}=\frac{-6}{10}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+28}{2*5}=\frac{50}{10}
=5
$