3x=(8x^2)-3

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

3x=(8x^2)-3

We move all terms to the left:

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

We get rid of parentheses

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

a = -8; b = 3; c = +3;
Δ = b2-4ac
Δ = 32-4·(-8)·3
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{105}}{2*-8}=\frac{-3-\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-8}=\frac{-3+\sqrt{105}}{-16}
$