4/5*x=20-x

Solution for 4/5*x=20-x equation:

4/5x=20-x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/5x+1x-20=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-100x+4=0

a = 5; b = -100; c = +4;
Δ = b2-4ac
Δ = -1002-4·5·4
Δ = 9920
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:

$\sqrt{\Delta}=\sqrt{9920}=\sqrt{64*155}=\sqrt{64}*\sqrt{155}=8\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-8\sqrt{155}}{2*5}=\frac{100-8\sqrt{155}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+8\sqrt{155}}{2*5}=\frac{100+8\sqrt{155}}{10}
$