x2+3x+1=7

Solution for x2+3x+1=7 equation:

x2+3x+1=7

We move all terms to the left:

x2+3x+1-(7)=0

We add all the numbers together, and all the variables

x^2+3x-6=0

a = 1; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·1·(-6)
Δ = 33
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{-(3)-\sqrt{33}}{2*1}=\frac{-3-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*1}=\frac{-3+\sqrt{33}}{2}
$