8x^2+6x+6=78

Solution for 8x^2+6x+6=78 equation:

8x^2+6x+6=78

We move all terms to the left:

8x^2+6x+6-(78)=0

We add all the numbers together, and all the variables

8x^2+6x-72=0

a = 8; b = 6; c = -72;
Δ = b2-4ac
Δ = 62-4·8·(-72)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{65}}{2*8}=\frac{-6-6\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{65}}{2*8}=\frac{-6+6\sqrt{65}}{16}
$