7x^2+2x+1=014

Solution for 7x^2+2x+1=014 equation:

7x^2+2x+1=014

We move all terms to the left:

7x^2+2x+1-(014)=0

We add all the numbers together, and all the variables

7x^2+2x-13=0

a = 7; b = 2; c = -13;
Δ = b2-4ac
Δ = 22-4·7·(-13)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{23}}{2*7}=\frac{-2-4\sqrt{23}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{23}}{2*7}=\frac{-2+4\sqrt{23}}{14}
$