4n^2-10n+3=-2

Solution for 4n^2-10n+3=-2 equation:

4n^2-10n+3=-2

We move all terms to the left:

4n^2-10n+3-(-2)=0

We add all the numbers together, and all the variables

4n^2-10n+5=0

a = 4; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·4·5
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*4}=\frac{10-2\sqrt{5}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*4}=\frac{10+2\sqrt{5}}{8}
$