x2+9x=14

Solution for x2+9x=14 equation:

x2+9x=14

We move all terms to the left:

x2+9x-(14)=0

We add all the numbers together, and all the variables

x^2+9x-14=0

a = 1; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·1·(-14)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{137}}{2*1}=\frac{-9-\sqrt{137}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{137}}{2*1}=\frac{-9+\sqrt{137}}{2}
$