x+2x(x+10)=66

Solution for x+2x(x+10)=66 equation:

x+2x(x+10)=66

We move all terms to the left:

x+2x(x+10)-(66)=0

We multiply parentheses

2x^2+x+20x-66=0

We add all the numbers together, and all the variables

2x^2+21x-66=0

a = 2; b = 21; c = -66;
Δ = b2-4ac
Δ = 212-4·2·(-66)
Δ = 969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{969}}{2*2}=\frac{-21-\sqrt{969}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{969}}{2*2}=\frac{-21+\sqrt{969}}{4}
$