2(x+6)+9x2=52

Solution for 2(x+6)+9x2=52 equation:

2(x+6)+9x^2=52

We move all terms to the left:

2(x+6)+9x^2-(52)=0

We multiply parentheses

9x^2+2x+12-52=0

We add all the numbers together, and all the variables

9x^2+2x-40=0

a = 9; b = 2; c = -40;
Δ = b2-4ac
Δ = 22-4·9·(-40)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*9}=\frac{-40}{18}
=-2+2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*9}=\frac{36}{18}
=2
$