(x+5)(2x+10)=33

Solution for (x+5)(2x+10)=33 equation:

(x+5)(2x+10)=33

We move all terms to the left:

(x+5)(2x+10)-(33)=0

We multiply parentheses ..

(+2x^2+10x+10x+50)-33=0

We get rid of parentheses

2x^2+10x+10x+50-33=0

We add all the numbers together, and all the variables

2x^2+20x+17=0

a = 2; b = 20; c = +17;
Δ = b2-4ac
Δ = 202-4·2·17
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{66}}{2*2}=\frac{-20-2\sqrt{66}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{66}}{2*2}=\frac{-20+2\sqrt{66}}{4}
$