224=(3x*3x)+(12*7x)

Solution for 224=(3x*3x)+(12*7x) equation:

224=(3x*3x)+(12*7x)

We move all terms to the left:

224-((3x*3x)+(12*7x))=0

We add all the numbers together, and all the variables

-((+3x*3x)+(+12*7x))+224=0


We calculate terms in parentheses: -((+3x*3x)+(+12*7x)), so:

(+3x*3x)+(+12*7x)

We get rid of parentheses

3x*3x+12*7x

Wy multiply elements

9x^2+84x

Back to the equation:

-(9x^2+84x)


We get rid of parentheses

-9x^2-84x+224=0

a = -9; b = -84; c = +224;
Δ = b2-4ac
Δ = -842-4·(-9)·224
Δ = 15120
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:

$\sqrt{\Delta}=\sqrt{15120}=\sqrt{144*105}=\sqrt{144}*\sqrt{105}=12\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{105}}{2*-9}=\frac{84-12\sqrt{105}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{105}}{2*-9}=\frac{84+12\sqrt{105}}{-18}
$