X^2+6x+3=7

Solution for X^2+6x+3=7 equation:

X^2+6X+3=7

We move all terms to the left:

X^2+6X+3-(7)=0

We add all the numbers together, and all the variables

X^2+6X-4=0

a = 1; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·1·(-4)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{13}}{2*1}=\frac{-6-2\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*1}=\frac{-6+2\sqrt{13}}{2}
$