2n(2n+5)=12

Solution for 2n(2n+5)=12 equation:

2n(2n+5)=12

We move all terms to the left:

2n(2n+5)-(12)=0

We multiply parentheses

4n^2+10n-12=0

a = 4; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·4·(-12)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{73}}{2*4}=\frac{-10-2\sqrt{73}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{73}}{2*4}=\frac{-10+2\sqrt{73}}{8}
$