14x^2+1=251

Solution for 14x^2+1=251 equation:

14x^2+1=251

We move all terms to the left:

14x^2+1-(251)=0

We add all the numbers together, and all the variables

14x^2-250=0

a = 14; b = 0; c = -250;
Δ = b2-4ac
Δ = 02-4·14·(-250)
Δ = 14000
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:

$\sqrt{\Delta}=\sqrt{14000}=\sqrt{400*35}=\sqrt{400}*\sqrt{35}=20\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{35}}{2*14}=\frac{0-20\sqrt{35}}{28}
=-\frac{20\sqrt{35}}{28}
=-\frac{5\sqrt{35}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{35}}{2*14}=\frac{0+20\sqrt{35}}{28}
=\frac{20\sqrt{35}}{28}
=\frac{5\sqrt{35}}{7}
$