84=14x^2+14x

Solution for 84=14x^2+14x equation:

84=14x^2+14x

We move all terms to the left:

84-(14x^2+14x)=0

We get rid of parentheses

-14x^2-14x+84=0

a = -14; b = -14; c = +84;
Δ = b2-4ac
Δ = -142-4·(-14)·84
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-70}{2*-14}=\frac{-56}{-28}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+70}{2*-14}=\frac{84}{-28}
=-3
$