4n(2n-7)=12

Solution for 4n(2n-7)=12 equation:

4n(2n-7)=12

We move all terms to the left:

4n(2n-7)-(12)=0

We multiply parentheses

8n^2-28n-12=0

a = 8; b = -28; c = -12;
Δ = b2-4ac
Δ = -282-4·8·(-12)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{73}}{2*8}=\frac{28-4\sqrt{73}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{73}}{2*8}=\frac{28+4\sqrt{73}}{16}
$