10=2x^2+12x+18

Solution for 10=2x^2+12x+18 equation:

10=2x^2+12x+18

We move all terms to the left:

10-(2x^2+12x+18)=0

We get rid of parentheses

-2x^2-12x-18+10=0

We add all the numbers together, and all the variables

-2x^2-12x-8=0

a = -2; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·(-2)·(-8)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{5}}{2*-2}=\frac{12-4\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{5}}{2*-2}=\frac{12+4\sqrt{5}}{-4}
$