2x^2+9=185

Solution for 2x^2+9=185 equation:

2x^2+9=185

We move all terms to the left:

2x^2+9-(185)=0

We add all the numbers together, and all the variables

2x^2-176=0

a = 2; b = 0; c = -176;
Δ = b2-4ac
Δ = 02-4·2·(-176)
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{22}}{2*2}=\frac{0-8\sqrt{22}}{4}
=-\frac{8\sqrt{22}}{4}
=-2\sqrt{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{22}}{2*2}=\frac{0+8\sqrt{22}}{4}
=\frac{8\sqrt{22}}{4}
=2\sqrt{22}
$