2x^2+9x+9+x^2-114=0

Solution for 2x^2+9x+9+x^2-114=0 equation:

2x^2+9x+9+x^2-114=0

We add all the numbers together, and all the variables

3x^2+9x-105=0

a = 3; b = 9; c = -105;
Δ = b2-4ac
Δ = 92-4·3·(-105)
Δ = 1341
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:

$\sqrt{\Delta}=\sqrt{1341}=\sqrt{9*149}=\sqrt{9}*\sqrt{149}=3\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{149}}{2*3}=\frac{-9-3\sqrt{149}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{149}}{2*3}=\frac{-9+3\sqrt{149}}{6}
$