X^2+7x+3=-1

Solution for X^2+7x+3=-1 equation:

X^2+7X+3=-1

We move all terms to the left:

X^2+7X+3-(-1)=0

We add all the numbers together, and all the variables

X^2+7X+4=0

a = 1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·1·4
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{-(7)-\sqrt{33}}{2*1}=\frac{-7-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*1}=\frac{-7+\sqrt{33}}{2}
$