3(x+1)4x+3=34

Solution for 3(x+1)4x+3=34 equation:

3(x+1)4x+3=34

We move all terms to the left:

3(x+1)4x+3-(34)=0

We add all the numbers together, and all the variables

3(x+1)4x-31=0

We multiply parentheses

12x^2+12x-31=0

a = 12; b = 12; c = -31;
Δ = b2-4ac
Δ = 122-4·12·(-31)
Δ = 1632
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{102}}{2*12}=\frac{-12-4\sqrt{102}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{102}}{2*12}=\frac{-12+4\sqrt{102}}{24}
$