333=x^2+x/2

Solution for 333=x^2+x/2 equation:

333=x^2+x/2

We move all terms to the left:

333-(x^2+x/2)=0

We get rid of parentheses

-x^2-x/2+333=0

We multiply all the terms by the denominator


-x^2*2-x+333*2=0

We add all the numbers together, and all the variables

-x^2*2-1x+666=0

Wy multiply elements

-2x^2-1x+666=0

a = -2; b = -1; c = +666;
Δ = b2-4ac
Δ = -12-4·(-2)·666
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-73}{2*-2}=\frac{-72}{-4}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+73}{2*-2}=\frac{74}{-4}
=-18+1/2
$