(x-12)(42-x)=224

Solution for (x-12)(42-x)=224 equation:

(x-12)(42-x)=224

We move all terms to the left:

(x-12)(42-x)-(224)=0

We add all the numbers together, and all the variables

(x-12)(-1x+42)-224=0

We multiply parentheses ..

(-1x^2+42x+12x-504)-224=0

We get rid of parentheses

-1x^2+42x+12x-504-224=0

We add all the numbers together, and all the variables

-1x^2+54x-728=0

a = -1; b = 54; c = -728;
Δ = b2-4ac
Δ = 542-4·(-1)·(-728)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2}{2*-1}=\frac{-56}{-2}
=+28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2}{2*-1}=\frac{-52}{-2}
=+26
$