75x^2-166x+80=0

Solution for 75x^2-166x+80=0 equation:

75x^2-166x+80=0

a = 75; b = -166; c = +80;
Δ = b2-4ac
Δ = -1662-4·75·80
Δ = 3556
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:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-2\sqrt{889}}{2*75}=\frac{166-2\sqrt{889}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+2\sqrt{889}}{2*75}=\frac{166+2\sqrt{889}}{150}
$