106=2x^2-5x+18

Solution for 106=2x^2-5x+18 equation:

106=2x^2-5x+18

We move all terms to the left:

106-(2x^2-5x+18)=0

We get rid of parentheses

-2x^2+5x-18+106=0

We add all the numbers together, and all the variables

-2x^2+5x+88=0

a = -2; b = 5; c = +88;
Δ = b2-4ac
Δ = 52-4·(-2)·88
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-27}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+27}{2*-2}=\frac{22}{-4}
=-5+1/2
$