25x^2-10x+1=43

Solution for 25x^2-10x+1=43 equation:

25x^2-10x+1=43

We move all terms to the left:

25x^2-10x+1-(43)=0

We add all the numbers together, and all the variables

25x^2-10x-42=0

a = 25; b = -10; c = -42;
Δ = b2-4ac
Δ = -102-4·25·(-42)
Δ = 4300
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:

$\sqrt{\Delta}=\sqrt{4300}=\sqrt{100*43}=\sqrt{100}*\sqrt{43}=10\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{43}}{2*25}=\frac{10-10\sqrt{43}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{43}}{2*25}=\frac{10+10\sqrt{43}}{50}
$