3X^2+6x+109=676

Solution for 3X^2+6x+109=676 equation:

3X^2+6X+109=676

We move all terms to the left:

3X^2+6X+109-(676)=0

We add all the numbers together, and all the variables

3X^2+6X-567=0

a = 3; b = 6; c = -567;
Δ = b2-4ac
Δ = 62-4·3·(-567)
Δ = 6840
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:

$\sqrt{\Delta}=\sqrt{6840}=\sqrt{36*190}=\sqrt{36}*\sqrt{190}=6\sqrt{190}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{190}}{2*3}=\frac{-6-6\sqrt{190}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{190}}{2*3}=\frac{-6+6\sqrt{190}}{6}
$