2u(3u+7)=34

Solution for 2u(3u+7)=34 equation:

2u(3u+7)=34

We move all terms to the left:

2u(3u+7)-(34)=0

We multiply parentheses

6u^2+14u-34=0

a = 6; b = 14; c = -34;
Δ = b2-4ac
Δ = 142-4·6·(-34)
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{253}}{2*6}=\frac{-14-2\sqrt{253}}{12}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{253}}{2*6}=\frac{-14+2\sqrt{253}}{12}
$