7x(2x-1)=9x-1

Solution for 7x(2x-1)=9x-1 equation:

7x(2x-1)=9x-1

We move all terms to the left:

7x(2x-1)-(9x-1)=0

We multiply parentheses

14x^2-7x-(9x-1)=0

We get rid of parentheses

14x^2-7x-9x+1=0

We add all the numbers together, and all the variables

14x^2-16x+1=0

a = 14; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·14·1
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10\sqrt{2}}{2*14}=\frac{16-10\sqrt{2}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10\sqrt{2}}{2*14}=\frac{16+10\sqrt{2}}{28}
$