X^2/3=4x-9

Solution for X^2/3=4x-9 equation:

X^2/3=4X-9

We move all terms to the left:

X^2/3-(4X-9)=0

We get rid of parentheses

X^2/3-4X+9=0

We multiply all the terms by the denominator


X^2-4X*3+9*3=0

We add all the numbers together, and all the variables

X^2-4X*3+27=0

Wy multiply elements

X^2-12X+27=0

a = 1; b = -12; c = +27;
Δ = b2-4ac
Δ = -122-4·1·27
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6}{2*1}=\frac{6}{2}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6}{2*1}=\frac{18}{2}
=9
$