2x^2+9x=(-5)

Solution for 2x^2+9x=(-5) equation:

2x^2+9x=(-5)

We move all terms to the left:

2x^2+9x-((-5))=0

We add all the numbers together, and all the variables

2x^2+9x+5=0

a = 2; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·2·5
Δ = 41
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{41}}{2*2}=\frac{-9-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*2}=\frac{-9+\sqrt{41}}{4}
$