169=2x2+14x

Solution for 169=2x2+14x equation:

169=2x^2+14x

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -14; c = +169;
Δ = b2-4ac
Δ = -142-4·(-2)·169
Δ = 1548
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1548}=\sqrt{36*43}=\sqrt{36}*\sqrt{43}=6\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{43}}{2*-2}=\frac{14-6\sqrt{43}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{43}}{2*-2}=\frac{14+6\sqrt{43}}{-4}
$