4n2-6n=10

Solution for 4n2-6n=10 equation:

4n^2-6n=10

We move all terms to the left:

4n^2-6n-(10)=0

a = 4; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·4·(-10)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*4}=\frac{-8}{8}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*4}=\frac{20}{8}
=2+1/2
$