169=2x^2+14x+49

Solution for 169=2x^2+14x+49 equation:

169=2x^2+14x+49

We move all terms to the left:

169-(2x^2+14x+49)=0

We get rid of parentheses

-2x^2-14x-49+169=0

We add all the numbers together, and all the variables

-2x^2-14x+120=0

a = -2; b = -14; c = +120;
Δ = b2-4ac
Δ = -142-4·(-2)·120
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-34}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+34}{2*-2}=\frac{48}{-4}
=-12
$