6x2-16=363x

Solution for 6x2-16=363x equation:

6x^2-16=363x

We move all terms to the left:

6x^2-16-(363x)=0

a = 6; b = -363; c = -16;
Δ = b2-4ac
Δ = -3632-4·6·(-16)
Δ = 132153
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:

$\sqrt{\Delta}=\sqrt{132153}=\sqrt{49*2697}=\sqrt{49}*\sqrt{2697}=7\sqrt{2697}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-363)-7\sqrt{2697}}{2*6}=\frac{363-7\sqrt{2697}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-363)+7\sqrt{2697}}{2*6}=\frac{363+7\sqrt{2697}}{12}
$