3n-2(10-n)n=10

Solution for 3n-2(10-n)n=10 equation:

3n-2(10-n)n=10

We move all terms to the left:

3n-2(10-n)n-(10)=0

We add all the numbers together, and all the variables

3n-2(-1n+10)n-10=0

We multiply parentheses

2n^2+3n-20n-10=0

We add all the numbers together, and all the variables

2n^2-17n-10=0

a = 2; b = -17; c = -10;
Δ = b2-4ac
Δ = -172-4·2·(-10)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{41}}{2*2}=\frac{17-3\sqrt{41}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{41}}{2*2}=\frac{17+3\sqrt{41}}{4}
$