3x(2+x)=14+x

Solution for 3x(2+x)=14+x equation:

3x(2+x)=14+x

We move all terms to the left:

3x(2+x)-(14+x)=0

We add all the numbers together, and all the variables

3x(x+2)-(x+14)=0

We multiply parentheses

3x^2+6x-(x+14)=0

We get rid of parentheses

3x^2+6x-x-14=0

We add all the numbers together, and all the variables

3x^2+5x-14=0

a = 3; b = 5; c = -14;
Δ = b2-4ac
Δ = 52-4·3·(-14)
Δ = 193
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{-(5)-\sqrt{193}}{2*3}=\frac{-5-\sqrt{193}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{193}}{2*3}=\frac{-5+\sqrt{193}}{6}
$