u(2u+9)=50

Solution for u(2u+9)=50 equation:

u(2u+9)=50

We move all terms to the left:

u(2u+9)-(50)=0

We multiply parentheses

2u^2+9u-50=0

a = 2; b = 9; c = -50;
Δ = b2-4ac
Δ = 92-4·2·(-50)
Δ = 481
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{481}}{2*2}=\frac{-9-\sqrt{481}}{4}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{481}}{2*2}=\frac{-9+\sqrt{481}}{4}
$