25x^2-10x+1=16

Solution for 25x^2-10x+1=16 equation:

25x^2-10x+1=16

We move all terms to the left:

25x^2-10x+1-(16)=0

We add all the numbers together, and all the variables

25x^2-10x-15=0

a = 25; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·25·(-15)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-40}{2*25}=\frac{-30}{50}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+40}{2*25}=\frac{50}{50}
=1
$