((20-8x)^(1/2))=x

Solution for ((20-8x)^(1/2))=x equation:

((20-8x)^(1/2))=x

We move all terms to the left:

((20-8x)^(1/2))-(x)=0

We add all the numbers together, and all the variables

((-8x+20)^(+1/2))-x=0

We add all the numbers together, and all the variables

-1x+((-8x+20)^(+1/2))=0

We multiply all the terms by the denominator


-1x*2))+((-8x+1+20)^(=0

We add all the numbers together, and all the variables

-1x*2))+((-8x+21)^(=0

We add all the numbers together, and all the variables

-8x-1x*2))+((=0

Wy multiply elements

-2x^2-8x=0

a = -2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-2}=\frac{16}{-4}
=-4
$