X=x^2+7x+3

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

X=X^2+7X+3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1X^2-6X-3=0

a = -1; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·(-1)·(-3)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6}}{2*-1}=\frac{6-2\sqrt{6}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6}}{2*-1}=\frac{6+2\sqrt{6}}{-2}
$