4n^2-7n+6=4

Solution for 4n^2-7n+6=4 equation:

4n^2-7n+6=4

We move all terms to the left:

4n^2-7n+6-(4)=0

We add all the numbers together, and all the variables

4n^2-7n+2=0

a = 4; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·4·2
Δ = 17
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{17}}{2*4}=\frac{7-\sqrt{17}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{17}}{2*4}=\frac{7+\sqrt{17}}{8}
$