x^2-3=-7x-x^2

Solution for x^2-3=-7x-x^2 equation:

x^2-3=-7x-x^2

We move all terms to the left:

x^2-3-(-7x-x^2)=0

We get rid of parentheses

x^2+x^2+7x-3=0

We add all the numbers together, and all the variables

2x^2+7x-3=0

a = 2; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·2·(-3)
Δ = 73
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{73}}{2*2}=\frac{-7-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*2}=\frac{-7+\sqrt{73}}{4}
$