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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+6x^2+15x-2x-5))+9x-1=0


We calculate terms in parentheses: -((+6x^2+15x-2x-5)), so:

(+6x^2+15x-2x-5)

We get rid of parentheses

6x^2+15x-2x-5

We add all the numbers together, and all the variables

6x^2+13x-5

Back to the equation:

-(6x^2+13x-5)


We add all the numbers together, and all the variables

9x-(6x^2+13x-5)-1=0

We get rid of parentheses

-6x^2+9x-13x+5-1=0

We add all the numbers together, and all the variables

-6x^2-4x+4=0

a = -6; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-6)·4
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-6}=\frac{4-4\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-6}=\frac{4+4\sqrt{7}}{-12}
$