4x+(2-x)^(1/2)=3

Solution for 4x+(2-x)^(1/2)=3 equation:

4x+(2-x)^(1/2)=3

We move all terms to the left:

4x+(2-x)^(1/2)-(3)=0

We add all the numbers together, and all the variables

4x+(-1x+2)^(+1/2)-3=0

We multiply all the terms by the denominator


4x*2)+(-1x+1+2)^(-3*2)=0

We add all the numbers together, and all the variables

4x*2)+(-1x+3)^(-6)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

8x^2-1x=0

a = 8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·8·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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