2x-3+4x(3x+2)=9x-1

Solution for 2x-3+4x(3x+2)=9x-1 equation:

2x-3+4x(3x+2)=9x-1

We move all terms to the left:

2x-3+4x(3x+2)-(9x-1)=0

We multiply parentheses

12x^2+2x+8x-(9x-1)-3=0

We get rid of parentheses

12x^2+2x+8x-9x+1-3=0

We add all the numbers together, and all the variables

12x^2+x-2=0

a = 12; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·12·(-2)
Δ = 97
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{97}}{2*12}=\frac{-1-\sqrt{97}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*12}=\frac{-1+\sqrt{97}}{24}
$