.5x+84=x2/3

Solution for .5x+84=x2/3 equation:

.5x+84=x2/3

We move all terms to the left:

.5x+84-(x2/3)=0

We add all the numbers together, and all the variables

.5x-(+x2/3)+84=0

We get rid of parentheses

.5x-x2/3+84=0

We multiply all the terms by the denominator


(.5x)*3-x2+84*3=0

We add all the numbers together, and all the variables

(+.5x)*3-x2+84*3=0

We add all the numbers together, and all the variables

-1x^2+(+.5x)*3+252=0

We multiply parentheses

-1x^2+3x+252=0

a = -1; b = 3; c = +252;
Δ = b2-4ac
Δ = 32-4·(-1)·252
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{113}}{2*-1}=\frac{-3-3\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{113}}{2*-1}=\frac{-3+3\sqrt{113}}{-2}
$