2x^2+14x=-17

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

2x^2+14x=-17

We move all terms to the left:

2x^2+14x-(-17)=0

We add all the numbers together, and all the variables

2x^2+14x+17=0

a = 2; b = 14; c = +17;
Δ = b2-4ac
Δ = 142-4·2·17
Δ = 60
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:

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