u^2+30u=19

Solution for u^2+30u=19 equation:

u^2+30u=19

We move all terms to the left:

u^2+30u-(19)=0

a = 1; b = 30; c = -19;
Δ = b2-4ac
Δ = 302-4·1·(-19)
Δ = 976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{61}}{2*1}=\frac{-30-4\sqrt{61}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{61}}{2*1}=\frac{-30+4\sqrt{61}}{2}
$