(54-5x)^(1/2)+8=x

Solution for (54-5x)^(1/2)+8=x equation:

(54-5x)^(1/2)+8=x

We move all terms to the left:

(54-5x)^(1/2)+8-(x)=0

We add all the numbers together, and all the variables

(-5x+54)^(+1/2)-x+8=0

We add all the numbers together, and all the variables

-1x+(-5x+54)^(+1/2)+8=0

We multiply all the terms by the denominator


-1x*2)+(-5x+1+54)^(+8*2)=0

We add all the numbers together, and all the variables

-1x*2)+(-5x+55)^16=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-2x^2-5x=0

a = -2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-2}=\frac{10}{-4}
=-2+1/2
$