289=2x^2-14x+49

Solution for 289=2x^2-14x+49 equation:

289=2x^2-14x+49

We move all terms to the left:

289-(2x^2-14x+49)=0

We get rid of parentheses

-2x^2+14x-49+289=0

We add all the numbers together, and all the variables

-2x^2+14x+240=0

a = -2; b = 14; c = +240;
Δ = b2-4ac
Δ = 142-4·(-2)·240
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-46}{2*-2}=\frac{-60}{-4}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+46}{2*-2}=\frac{32}{-4}
=-8
$