2n^2-20n+15=10

Solution for 2n^2-20n+15=10 equation:

2n^2-20n+15=10

We move all terms to the left:

2n^2-20n+15-(10)=0

We add all the numbers together, and all the variables

2n^2-20n+5=0

a = 2; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·2·5
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*2}=\frac{20-6\sqrt{10}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*2}=\frac{20+6\sqrt{10}}{4}
$