(-4w+21)^(1/2)=w

Solution for (-4w+21)^(1/2)=w equation:

(-4w+21)^(1/2)=w

We move all terms to the left:

(-4w+21)^(1/2)-(w)=0

We add all the numbers together, and all the variables

(-4w+21)^(+1/2)-w=0

We add all the numbers together, and all the variables

-1w+(-4w+21)^(+1/2)=0

We multiply all the terms by the denominator


-1w*2)+(-4w+1+21)^(=0

We add all the numbers together, and all the variables

-1w*2)+(-4w+22)^(=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-2w^2-4w=0

a = -2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-2)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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