2n^2-12n=10=0

Solution for 2n^2-12n=10=0 equation:

2n^2-12n=10=0

We move all terms to the left:

2n^2-12n-(10)=0

a = 2; b = -12; c = -10;
Δ = b2-4ac
Δ = -122-4·2·(-10)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{14}}{2*2}=\frac{12-4\sqrt{14}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{14}}{2*2}=\frac{12+4\sqrt{14}}{4}
$