9x(x-1)-7=0

Solution for 9x(x-1)-7=0 equation:

9x(x-1)-7=0

We multiply parentheses

9x^2-9x-7=0

a = 9; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·9·(-7)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{37}}{2*9}=\frac{9-3\sqrt{37}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{37}}{2*9}=\frac{9+3\sqrt{37}}{18}
$