66=x+x^2+(x-4)

Solution for 66=x+x^2+(x-4) equation:

66=x+x^2+(x-4)

We move all terms to the left:

66-(x+x^2+(x-4))=0


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

x+x^2+(x-4)

determiningTheFunctionDomain
x^2+x+(x-4)

We get rid of parentheses

x^2+x+x-4

We add all the numbers together, and all the variables

x^2+2x-4

Back to the equation:

-(x^2+2x-4)


We get rid of parentheses

-x^2-2x+4+66=0

We add all the numbers together, and all the variables

-1x^2-2x+70=0

a = -1; b = -2; c = +70;
Δ = b2-4ac
Δ = -22-4·(-1)·70
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{71}}{2*-1}=\frac{2-2\sqrt{71}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{71}}{2*-1}=\frac{2+2\sqrt{71}}{-2}
$