25x^2-166x+256=0

Solution for 25x^2-166x+256=0 equation:

25x^2-166x+256=0

a = 25; b = -166; c = +256;
Δ = b2-4ac
Δ = -1662-4·25·256
Δ = 1956
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:

$\sqrt{\Delta}=\sqrt{1956}=\sqrt{4*489}=\sqrt{4}*\sqrt{489}=2\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-166)-2\sqrt{489}}{2*25}=\frac{166-2\sqrt{489}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-166)+2\sqrt{489}}{2*25}=\frac{166+2\sqrt{489}}{50}
$