6x+3=(72-72x)^(1/2)

Solution for 6x+3=(72-72x)^(1/2) equation:

6x+3=(72-72x)^(1/2)

We move all terms to the left:

6x+3-((72-72x)^(1/2))=0

We add all the numbers together, and all the variables

6x-((-72x+72)^(+1/2))+3=0

We multiply all the terms by the denominator


6x*2))-((-72x+1+72)^(+3*2))=0

We add all the numbers together, and all the variables

6x*2))-((-72x+73)^6)=0

We add all the numbers together, and all the variables

-72x+6x*2))-((=0

Wy multiply elements

12x^2-72x=0

a = 12; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·12·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*12}=\frac{144}{24}
=6
$