5x^2-28x+16=0

Solution for 5x^2-28x+16=0 equation:

5x^2-28x+16=0

a = 5; b = -28; c = +16;
Δ = b2-4ac
Δ = -282-4·5·16
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{29}}{2*5}=\frac{28-4\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{29}}{2*5}=\frac{28+4\sqrt{29}}{10}
$