0.5n(10n+20)=10+5n

Solution for 0.5n(10n+20)=10+5n equation:

0.5n(10n+20)=10+5n

We move all terms to the left:

0.5n(10n+20)-(10+5n)=0

We add all the numbers together, and all the variables

0.5n(10n+20)-(5n+10)=0

We multiply parentheses

0n^2+0n-(5n+10)=0

We get rid of parentheses

0n^2+0n-5n-10=0

We add all the numbers together, and all the variables

n^2-4n-10=0

a = 1; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·1·(-10)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*1}=\frac{4-2\sqrt{14}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*1}=\frac{4+2\sqrt{14}}{2}
$