60x^2-105x+40=0

Solution for 60x^2-105x+40=0 equation:

60x^2-105x+40=0

a = 60; b = -105; c = +40;
Δ = b2-4ac
Δ = -1052-4·60·40
Δ = 1425
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:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-5\sqrt{57}}{2*60}=\frac{105-5\sqrt{57}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+5\sqrt{57}}{2*60}=\frac{105+5\sqrt{57}}{120}
$