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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((3x-1)2), so:

(3x-1)2

We multiply parentheses

6x-2

Back to the equation:

-(6x-2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

9x^2-11x+2=0

a = 9; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·9·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*9}=\frac{4}{18}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*9}=\frac{18}{18}
=1
$