199=2x^2-x-1

Solution for 199=2x^2-x-1 equation:

199=2x^2-x-1

We move all terms to the left:

199-(2x^2-x-1)=0

We get rid of parentheses

-2x^2+x+1+199=0

We add all the numbers together, and all the variables

-2x^2+x+200=0

a = -2; b = 1; c = +200;
Δ = b2-4ac
Δ = 12-4·(-2)·200
Δ = 1601
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{-(1)-\sqrt{1601}}{2*-2}=\frac{-1-\sqrt{1601}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1601}}{2*-2}=\frac{-1+\sqrt{1601}}{-4}
$