105=2x^2+x

Solution for 105=2x^2+x equation:

105=2x^2+x

We move all terms to the left:

105-(2x^2+x)=0

We get rid of parentheses

-2x^2-x+105=0

We add all the numbers together, and all the variables

-2x^2-1x+105=0

a = -2; b = -1; c = +105;
Δ = b2-4ac
Δ = -12-4·(-2)·105
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-29}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*-2}=\frac{30}{-4}
=-7+1/2
$