5x^2+2x+1=7

Solution for 5x^2+2x+1=7 equation:

5x^2+2x+1=7

We move all terms to the left:

5x^2+2x+1-(7)=0

We add all the numbers together, and all the variables

5x^2+2x-6=0

a = 5; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·5·(-6)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*5}=\frac{-2-2\sqrt{31}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*5}=\frac{-2+2\sqrt{31}}{10}
$