0=2x^2+7x+1

Solution for 0=2x^2+7x+1 equation:

0=2x^2+7x+1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2-7x-1=0

a = -2; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·(-2)·(-1)
Δ = 41
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{-(-7)-\sqrt{41}}{2*-2}=\frac{7-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{41}}{2*-2}=\frac{7+\sqrt{41}}{-4}
$