x+12=28-2x(x-4)

Solution for x+12=28-2x(x-4) equation:

x+12=28-2x(x-4)

We move all terms to the left:

x+12-(28-2x(x-4))=0


We calculate terms in parentheses: -(28-2x(x-4)), so:

28-2x(x-4)

determiningTheFunctionDomain
-2x(x-4)+28

We multiply parentheses

-2x^2+8x+28

Back to the equation:

-(-2x^2+8x+28)


We get rid of parentheses

2x^2-8x+x-28+12=0

We add all the numbers together, and all the variables

2x^2-7x-16=0

a = 2; b = -7; c = -16;
Δ = b2-4ac
Δ = -72-4·2·(-16)
Δ = 177
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{177}}{2*2}=\frac{7-\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*2}=\frac{7+\sqrt{177}}{4}
$