n^2=17n+70

Solution for n^2=17n+70 equation:

n^2=17n+70

We move all terms to the left:

n^2-(17n+70)=0

We get rid of parentheses

n^2-17n-70=0

a = 1; b = -17; c = -70;
Δ = b2-4ac
Δ = -172-4·1·(-70)
Δ = 569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{569}}{2*1}=\frac{17-\sqrt{569}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{569}}{2*1}=\frac{17+\sqrt{569}}{2}
$