-1+9x=4x^2

Solution for -1+9x=4x^2 equation:

-1+9x=4x^2

We move all terms to the left:

-1+9x-(4x^2)=0

determiningTheFunctionDomain
-4x^2+9x-1=0

a = -4; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-4)·(-1)
Δ = 65
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{-(9)-\sqrt{65}}{2*-4}=\frac{-9-\sqrt{65}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{65}}{2*-4}=\frac{-9+\sqrt{65}}{-8}
$