X^2+6x+109=676

Solution for X^2+6x+109=676 equation:

X^2+6X+109=676

We move all terms to the left:

X^2+6X+109-(676)=0

We add all the numbers together, and all the variables

X^2+6X-567=0

a = 1; b = 6; c = -567;
Δ = b2-4ac
Δ = 62-4·1·(-567)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-48}{2*1}=\frac{-54}{2}
=-27
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+48}{2*1}=\frac{42}{2}
=21
$