2x^2=-7x-1

Solution for 2x^2=-7x-1 equation:

2x^2=-7x-1

We move all terms to the left:

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}
$