5x^2-16x+9=0

Solution for 5x^2-16x+9=0 equation:

5x^2-16x+9=0

a = 5; b = -16; c = +9;
Δ = b2-4ac
Δ = -162-4·5·9
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{19}}{2*5}=\frac{16-2\sqrt{19}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{19}}{2*5}=\frac{16+2\sqrt{19}}{10}
$