9x^2-4x+4=5x+3

Solution for 9x^2-4x+4=5x+3 equation:

9x^2-4x+4=5x+3

We move all terms to the left:

9x^2-4x+4-(5x+3)=0

We get rid of parentheses

9x^2-4x-5x-3+4=0

We add all the numbers together, and all the variables

9x^2-9x+1=0

a = 9; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·9·1
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{5}}{2*9}=\frac{9-3\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{5}}{2*9}=\frac{9+3\sqrt{5}}{18}
$