x(x+30)+2x=33

Solution for x(x+30)+2x=33 equation:

x(x+30)+2x=33

We move all terms to the left:

x(x+30)+2x-(33)=0

We add all the numbers together, and all the variables

2x+x(x+30)-33=0

We multiply parentheses

x^2+2x+30x-33=0

We add all the numbers together, and all the variables

x^2+32x-33=0

a = 1; b = 32; c = -33;
Δ = b2-4ac
Δ = 322-4·1·(-33)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-34}{2*1}=\frac{-66}{2}
=-33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+34}{2*1}=\frac{2}{2}
=1
$