19x^2-120x+72=0

Solution for 19x^2-120x+72=0 equation:

19x^2-120x+72=0

a = 19; b = -120; c = +72;
Δ = b2-4ac
Δ = -1202-4·19·72
Δ = 8928
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:

$\sqrt{\Delta}=\sqrt{8928}=\sqrt{144*62}=\sqrt{144}*\sqrt{62}=12\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-12\sqrt{62}}{2*19}=\frac{120-12\sqrt{62}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+12\sqrt{62}}{2*19}=\frac{120+12\sqrt{62}}{38}
$