19x^2-60x+19=0

Solution for 19x^2-60x+19=0 equation:

19x^2-60x+19=0

a = 19; b = -60; c = +19;
Δ = b2-4ac
Δ = -602-4·19·19
Δ = 2156
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:

$\sqrt{\Delta}=\sqrt{2156}=\sqrt{196*11}=\sqrt{196}*\sqrt{11}=14\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-14\sqrt{11}}{2*19}=\frac{60-14\sqrt{11}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+14\sqrt{11}}{2*19}=\frac{60+14\sqrt{11}}{38}
$