(x+4)+34x+x^2-x^=-32

Solution for (x+4)+34x+x^2-x^=-32 equation:

(x+4)+34x+x^2-x^=-32

We move all terms to the left:

(x+4)+34x+x^2-x^-(-32)=0

We add all the numbers together, and all the variables

x^2+33x+(x+4)+32=0

We get rid of parentheses

x^2+33x+x+4+32=0

We add all the numbers together, and all the variables

x^2+34x+36=0

a = 1; b = 34; c = +36;
Δ = b2-4ac
Δ = 342-4·1·36
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{253}}{2*1}=\frac{-34-2\sqrt{253}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{253}}{2*1}=\frac{-34+2\sqrt{253}}{2}
$