2x^2+2x-1=252

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

2x^2+2x-1=252

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2+2x-253=0

a = 2; b = 2; c = -253;
Δ = b2-4ac
Δ = 22-4·2·(-253)
Δ = 2028
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2028}=\sqrt{676*3}=\sqrt{676}*\sqrt{3}=26\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-26\sqrt{3}}{2*2}=\frac{-2-26\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+26\sqrt{3}}{2*2}=\frac{-2+26\sqrt{3}}{4}
$