(-3x+10)^(1/2)=x

Solution for (-3x+10)^(1/2)=x equation:

(-3x+10)^(1/2)=x

We move all terms to the left:

(-3x+10)^(1/2)-(x)=0

We add all the numbers together, and all the variables

(-3x+10)^(+1/2)-x=0

We add all the numbers together, and all the variables

-1x+(-3x+10)^(+1/2)=0

We multiply all the terms by the denominator


-1x*2)+(-3x+1+10)^(=0

We add all the numbers together, and all the variables

-1x*2)+(-3x+11)^(=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-2x^2-3x=0

a = -2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-2)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-2}=\frac{6}{-4}
=-1+1/2
$