2x^2-14x=169

Solution for 2x^2-14x=169 equation:

2x^2-14x=169

We move all terms to the left:

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}
$