3x=5x^2+9x-1

Solution for 3x=5x^2+9x-1 equation:

3x=5x^2+9x-1

We move all terms to the left:

3x-(5x^2+9x-1)=0

We get rid of parentheses

-5x^2+3x-9x+1=0

We add all the numbers together, and all the variables

-5x^2-6x+1=0

a = -5; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-5)·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{14}}{2*-5}=\frac{6-2\sqrt{14}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{14}}{2*-5}=\frac{6+2\sqrt{14}}{-10}
$