14s^2-77s+84=0

Solution for 14s^2-77s+84=0 equation:

14s^2-77s+84=0

a = 14; b = -77; c = +84;
Δ = b2-4ac
Δ = -772-4·14·84
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-35}{2*14}=\frac{42}{28}
=1+1/2
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+35}{2*14}=\frac{112}{28}
=4
$