-1/4x+20=-x+5

Solution for -1/4x+20=-x+5 equation:

-1/4x+20=-x+5

We move all terms to the left:

-1/4x+20-(-x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x-(-1x+5)+20=0

We get rid of parentheses

-1/4x+1x-5+20=0

We multiply all the terms by the denominator


1x*4x-5*4x+20*4x-1=0

Wy multiply elements

4x^2-20x+80x-1=0

We add all the numbers together, and all the variables

4x^2+60x-1=0

a = 4; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·4·(-1)
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{226}}{2*4}=\frac{-60-4\sqrt{226}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{226}}{2*4}=\frac{-60+4\sqrt{226}}{8}
$