3n(n-7)=15

Solution for 3n(n-7)=15 equation:

3n(n-7)=15

We move all terms to the left:

3n(n-7)-(15)=0

We multiply parentheses

3n^2-21n-15=0

a = 3; b = -21; c = -15;
Δ = b2-4ac
Δ = -212-4·3·(-15)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{69}}{2*3}=\frac{21-3\sqrt{69}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{69}}{2*3}=\frac{21+3\sqrt{69}}{6}
$