3u2+14u=8

Solution for 3u2+14u=8 equation:

3u^2+14u=8

We move all terms to the left:

3u^2+14u-(8)=0

a = 3; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·3·(-8)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{73}}{2*3}=\frac{-14-2\sqrt{73}}{6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{73}}{2*3}=\frac{-14+2\sqrt{73}}{6}
$