2x(x+6)=224

Solution for 2x(x+6)=224 equation:

2x(x+6)=224

We move all terms to the left:

2x(x+6)-(224)=0

We multiply parentheses

2x^2+12x-224=0

a = 2; b = 12; c = -224;
Δ = b2-4ac
Δ = 122-4·2·(-224)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-44}{2*2}=\frac{-56}{4}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+44}{2*2}=\frac{32}{4}
=8
$