3x(x+2)=112

Solution for 3x(x+2)=112 equation:

3x(x+2)=112

We move all terms to the left:

3x(x+2)-(112)=0

We multiply parentheses

3x^2+6x-112=0

a = 3; b = 6; c = -112;
Δ = b2-4ac
Δ = 62-4·3·(-112)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{345}}{2*3}=\frac{-6-2\sqrt{345}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{345}}{2*3}=\frac{-6+2\sqrt{345}}{6}
$