15x^2-80x+40=0

Solution for 15x^2-80x+40=0 equation:

15x^2-80x+40=0

a = 15; b = -80; c = +40;
Δ = b2-4ac
Δ = -802-4·15·40
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{10}}{2*15}=\frac{80-20\sqrt{10}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{10}}{2*15}=\frac{80+20\sqrt{10}}{30}
$