45x^2-50x+9=0

Solution for 45x^2-50x+9=0 equation:

45x^2-50x+9=0

a = 45; b = -50; c = +9;
Δ = b2-4ac
Δ = -502-4·45·9
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-4\sqrt{55}}{2*45}=\frac{50-4\sqrt{55}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+4\sqrt{55}}{2*45}=\frac{50+4\sqrt{55}}{90}
$