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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2+4x+3x-31=0

We add all the numbers together, and all the variables

3x^2+7x-31=0

a = 3; b = 7; c = -31;
Δ = b2-4ac
Δ = 72-4·3·(-31)
Δ = 421
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{421}}{2*3}=\frac{-7-\sqrt{421}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{421}}{2*3}=\frac{-7+\sqrt{421}}{6}
$