(1/4)(x-5)=5-x

Solution for (1/4)(x-5)=5-x equation:

(1/4)(x-5)=5-x

We move all terms to the left:

(1/4)(x-5)-(5-x)=0


Domain of the equation: 4)(x-5)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(x-5)-(-1x+5)=0

We get rid of parentheses

(+1/4)(x-5)+1x-5=0

We multiply parentheses ..

(+x^2+1/4*-5)+1x-5=0

We multiply all the terms by the denominator


(+x^2+1+1x*4*-5)-5*4*-5)=0

We add all the numbers together, and all the variables

(+x^2+1+1x*4*-5)=0

We get rid of parentheses

x^2+1x*4*+1-5=0

We add all the numbers together, and all the variables

x^2+1x*4*-4=0

Wy multiply elements

x^2+4x^2-4=0

We add all the numbers together, and all the variables

5x^2-4=0

a = 5; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·5·(-4)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*5}=\frac{0-4\sqrt{5}}{10}
=-\frac{4\sqrt{5}}{10}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*5}=\frac{0+4\sqrt{5}}{10}
=\frac{4\sqrt{5}}{10}
=\frac{2\sqrt{5}}{5}
$