5x2-28x+19=0

Solution for 5x2-28x+19=0 equation:

5x^2-28x+19=0

a = 5; b = -28; c = +19;
Δ = b2-4ac
Δ = -282-4·5·19
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{101}}{2*5}=\frac{28-2\sqrt{101}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{101}}{2*5}=\frac{28+2\sqrt{101}}{10}
$