(x+(x*x)+(x-4))=66

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

(x+(x*x)+(x-4))=66

We move all terms to the left:

(x+(x*x)+(x-4))-(66)=0

We add all the numbers together, and all the variables

(x+(+x*x)+(x-4))-66=0


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

x+(+x*x)+(x-4)

We get rid of parentheses

x+x*x+x-4

We add all the numbers together, and all the variables

2x+x*x-4

Wy multiply elements

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

x^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}
$