9x^2-4x+4=129

Solution for 9x^2-4x+4=129 equation:

9x^2-4x+4=129

We move all terms to the left:

9x^2-4x+4-(129)=0

We add all the numbers together, and all the variables

9x^2-4x-125=0

a = 9; b = -4; c = -125;
Δ = b2-4ac
Δ = -42-4·9·(-125)
Δ = 4516
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:

$\sqrt{\Delta}=\sqrt{4516}=\sqrt{4*1129}=\sqrt{4}*\sqrt{1129}=2\sqrt{1129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{1129}}{2*9}=\frac{4-2\sqrt{1129}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{1129}}{2*9}=\frac{4+2\sqrt{1129}}{18}
$