7n^2=-45n-70

Solution for 7n^2=-45n-70 equation:

7n^2=-45n-70

We move all terms to the left:

7n^2-(-45n-70)=0

We get rid of parentheses

7n^2+45n+70=0

a = 7; b = 45; c = +70;
Δ = b2-4ac
Δ = 452-4·7·70
Δ = 65
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{-(45)-\sqrt{65}}{2*7}=\frac{-45-\sqrt{65}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{65}}{2*7}=\frac{-45+\sqrt{65}}{14}
$