6-8x=3x^2-1

Solution for 6-8x=3x^2-1 equation:

6-8x=3x^2-1

We move all terms to the left:

6-8x-(3x^2-1)=0

We get rid of parentheses

-3x^2-8x+1+6=0

We add all the numbers together, and all the variables

-3x^2-8x+7=0

a = -3; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-3)·7
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{37}}{2*-3}=\frac{8-2\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{37}}{2*-3}=\frac{8+2\sqrt{37}}{-6}
$