x+x2/3=45

Solution for x+x2/3=45 equation:

x+x2/3=45

We move all terms to the left:

x+x2/3-(45)=0

We multiply all the terms by the denominator


x*3+x2-45*3=0

We add all the numbers together, and all the variables

x^2+x*3-135=0

Wy multiply elements

x^2+3x-135=0

a = 1; b = 3; c = -135;
Δ = b2-4ac
Δ = 32-4·1·(-135)
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{61}}{2*1}=\frac{-3-3\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{61}}{2*1}=\frac{-3+3\sqrt{61}}{2}
$