x=6+(28-3x)^(1/2)

Solution for x=6+(28-3x)^(1/2) equation:

x=6+(28-3x)^(1/2)

We move all terms to the left:

x-(6+(28-3x)^(1/2))=0

We add all the numbers together, and all the variables

x-(6+(-3x+28)^(+1/2))=0

We multiply all the terms by the denominator


x*2))-(6+(-3x+1+28)^(=0

We add all the numbers together, and all the variables

x*2))-(6+(-3x+29)^(=0

We add all the numbers together, and all the variables

-3x+x*2))-(6+(=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
$