4n^2=7n+102

Solution for 4n^2=7n+102 equation:

4n^2=7n+102

We move all terms to the left:

4n^2-(7n+102)=0

We get rid of parentheses

4n^2-7n-102=0

a = 4; b = -7; c = -102;
Δ = b2-4ac
Δ = -72-4·4·(-102)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-41}{2*4}=\frac{-34}{8}
=-4+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+41}{2*4}=\frac{48}{8}
=6
$