u(3u+4)=3u+4

Solution for u(3u+4)=3u+4 equation:

u(3u+4)=3u+4

We move all terms to the left:

u(3u+4)-(3u+4)=0

We multiply parentheses

3u^2+4u-(3u+4)=0

We get rid of parentheses

3u^2+4u-3u-4=0

We add all the numbers together, and all the variables

3u^2+u-4=0

a = 3; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·3·(-4)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*3}=\frac{-8}{6}
=-1+1/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*3}=\frac{6}{6}
=1
$