2x^2+14x+49=17^2

Solution for 2x^2+14x+49=17^2 equation:

2x^2+14x+49=17^2

We move all terms to the left:

2x^2+14x+49-(17^2)=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
$