x^2-51=-14x

Solution for x^2-51=-14x equation:

x^2-51=-14x

We move all terms to the left:

x^2-51-(-14x)=0

We get rid of parentheses

x^2+14x-51=0

a = 1; b = 14; c = -51;
Δ = b2-4ac
Δ = 142-4·1·(-51)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-20}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+20}{2*1}=\frac{6}{2}
=3
$