x=4x^2-9

Solution for x=4x^2-9 equation:

x=4x^2-9

We move all terms to the left:

x-(4x^2-9)=0

We get rid of parentheses

-4x^2+x+9=0

a = -4; b = 1; c = +9;
Δ = b2-4ac
Δ = 12-4·(-4)·9
Δ = 145
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{-(1)-\sqrt{145}}{2*-4}=\frac{-1-\sqrt{145}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*-4}=\frac{-1+\sqrt{145}}{-8}
$