2x2+14x=-9

Solution for 2x2+14x=-9 equation:

2x^2+14x=-9

We move all terms to the left:

2x^2+14x-(-9)=0

We add all the numbers together, and all the variables

2x^2+14x+9=0

a = 2; b = 14; c = +9;
Δ = b2-4ac
Δ = 142-4·2·9
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{31}}{2*2}=\frac{-14-2\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{31}}{2*2}=\frac{-14+2\sqrt{31}}{4}
$