7n^2-70n=-112

Solution for 7n^2-70n=-112 equation:

7n^2-70n=-112

We move all terms to the left:

7n^2-70n-(-112)=0

We add all the numbers together, and all the variables

7n^2-70n+112=0

a = 7; b = -70; c = +112;
Δ = b2-4ac
Δ = -702-4·7·112
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-42}{2*7}=\frac{28}{14}
=2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+42}{2*7}=\frac{112}{14}
=8
$