2u^2+9u=u^2+2

Solution for 2u^2+9u=u^2+2 equation:

2u^2+9u=u^2+2

We move all terms to the left:

2u^2+9u-(u^2+2)=0

We get rid of parentheses

2u^2-u^2+9u-2=0

We add all the numbers together, and all the variables

u^2+9u-2=0

a = 1; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·1·(-2)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{89}}{2*1}=\frac{-9-\sqrt{89}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{89}}{2*1}=\frac{-9+\sqrt{89}}{2}
$