x^2-4x+4=16/25

Solution for x^2-4x+4=16/25 equation:

x^2-4x+4=16/25

We move all terms to the left:

x^2-4x+4-(16/25)=0

We add all the numbers together, and all the variables

x^2-4x+4-(+16/25)=0

We get rid of parentheses

x^2-4x+4-16/25=0

We multiply all the terms by the denominator


x^2*25-4x*25-16+4*25=0

We add all the numbers together, and all the variables

x^2*25-4x*25+84=0

Wy multiply elements

25x^2-100x+84=0

a = 25; b = -100; c = +84;
Δ = b2-4ac
Δ = -1002-4·25·84
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{-(-100)-40}{2*25}=\frac{60}{50}
=1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+40}{2*25}=\frac{140}{50}
=2+4/5
$