x^2+x-3=65

Solution for x^2+x-3=65 equation:

x^2+x-3=65

We move all terms to the left:

x^2+x-3-(65)=0

We add all the numbers together, and all the variables

x^2+x-68=0

a = 1; b = 1; c = -68;
Δ = b2-4ac
Δ = 12-4·1·(-68)
Δ = 273
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{273}}{2*1}=\frac{-1-\sqrt{273}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{273}}{2*1}=\frac{-1+\sqrt{273}}{2}
$