5n^2-20n+20=7

Solution for 5n^2-20n+20=7 equation:

5n^2-20n+20=7

We move all terms to the left:

5n^2-20n+20-(7)=0

We add all the numbers together, and all the variables

5n^2-20n+13=0

a = 5; b = -20; c = +13;
Δ = b2-4ac
Δ = -202-4·5·13
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{35}}{2*5}=\frac{20-2\sqrt{35}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{35}}{2*5}=\frac{20+2\sqrt{35}}{10}
$