138=2x^2+9x+10

Solution for 138=2x^2+9x+10 equation:

138=2x^2+9x+10

We move all terms to the left:

138-(2x^2+9x+10)=0

We get rid of parentheses

-2x^2-9x-10+138=0

We add all the numbers together, and all the variables

-2x^2-9x+128=0

a = -2; b = -9; c = +128;
Δ = b2-4ac
Δ = -92-4·(-2)·128
Δ = 1105
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{-(-9)-\sqrt{1105}}{2*-2}=\frac{9-\sqrt{1105}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{1105}}{2*-2}=\frac{9+\sqrt{1105}}{-4}
$