2x^2+x-1=252

Solution for 2x^2+x-1=252 equation:

2x^2+x-1=252

We move all terms to the left:

2x^2+x-1-(252)=0

We add all the numbers together, and all the variables

2x^2+x-253=0

a = 2; b = 1; c = -253;
Δ = b2-4ac
Δ = 12-4·2·(-253)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-45}{2*2}=\frac{-46}{4}
=-11+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+45}{2*2}=\frac{44}{4}
=11
$