224=3x^2+12+7x

Solution for 224=3x^2+12+7x equation:

224=3x^2+12+7x

We move all terms to the left:

224-(3x^2+12+7x)=0

We get rid of parentheses

-3x^2-7x-12+224=0

We add all the numbers together, and all the variables

-3x^2-7x+212=0

a = -3; b = -7; c = +212;
Δ = b2-4ac
Δ = -72-4·(-3)·212
Δ = 2593
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{2593}}{2*-3}=\frac{7-\sqrt{2593}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2593}}{2*-3}=\frac{7+\sqrt{2593}}{-6}
$