6x^2+7=385

Solution for 6x^2+7=385 equation:

6x^2+7=385

We move all terms to the left:

6x^2+7-(385)=0

We add all the numbers together, and all the variables

6x^2-378=0

a = 6; b = 0; c = -378;
Δ = b2-4ac
Δ = 02-4·6·(-378)
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{7}}{2*6}=\frac{0-36\sqrt{7}}{12}
=-\frac{36\sqrt{7}}{12}
=-3\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{7}}{2*6}=\frac{0+36\sqrt{7}}{12}
=\frac{36\sqrt{7}}{12}
=3\sqrt{7}
$