75x^2-766x+80=0

Solution for 75x^2-766x+80=0 equation:

75x^2-766x+80=0

a = 75; b = -766; c = +80;
Δ = b2-4ac
Δ = -7662-4·75·80
Δ = 562756
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:

$\sqrt{\Delta}=\sqrt{562756}=\sqrt{4*140689}=\sqrt{4}*\sqrt{140689}=2\sqrt{140689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-766)-2\sqrt{140689}}{2*75}=\frac{766-2\sqrt{140689}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-766)+2\sqrt{140689}}{2*75}=\frac{766+2\sqrt{140689}}{150}
$