4n^2-4=7n

Solution for 4n^2-4=7n equation:

4n^2-4=7n

We move all terms to the left:

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

a = 4; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·4·(-4)
Δ = 113
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{-(-7)-\sqrt{113}}{2*4}=\frac{7-\sqrt{113}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{113}}{2*4}=\frac{7+\sqrt{113}}{8}
$