8(x)=3x^2-1

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

8(x)=3x^2-1

We move all terms to the left:

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

We get rid of parentheses

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

a = -3; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-3)·1
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*-3}=\frac{-8-2\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*-3}=\frac{-8+2\sqrt{19}}{-6}
$