6x^2+92x+7=-209

Solution for 6x^2+92x+7=-209 equation:

6x^2+92x+7=-209

We move all terms to the left:

6x^2+92x+7-(-209)=0

We add all the numbers together, and all the variables

6x^2+92x+216=0

a = 6; b = 92; c = +216;
Δ = b2-4ac
Δ = 922-4·6·216
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{205}}{2*6}=\frac{-92-4\sqrt{205}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{205}}{2*6}=\frac{-92+4\sqrt{205}}{12}
$