X^2-4x+4=5/2+4

Solution for X^2-4x+4=5/2+4 equation:

X^2-4X+4=5/2+4

We move all terms to the left:

X^2-4X+4-(5/2+4)=0

We get rid of parentheses

X^2-4X+4-4-5/2=0

We multiply all the terms by the denominator


X^2*2-4X*2-5+4*2-4*2=0

We add all the numbers together, and all the variables

X^2*2-4X*2-5=0

Wy multiply elements

2X^2-8X-5=0

a = 2; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·2·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*2}=\frac{8-2\sqrt{26}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*2}=\frac{8+2\sqrt{26}}{4}
$