2/3*x=40

Solution for 2/3*x=40 equation:

2/3*x=40

We move all terms to the left:

2/3*x-(40)=0


Domain of the equation: 3*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-40*3*x+2=0

Wy multiply elements

-120x*x+2=0

Wy multiply elements

-120x^2+2=0

a = -120; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-120)·2
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-120}=\frac{0-8\sqrt{15}}{-240}
=-\frac{8\sqrt{15}}{-240}
=-\frac{\sqrt{15}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-120}=\frac{0+8\sqrt{15}}{-240}
=\frac{8\sqrt{15}}{-240}
=\frac{\sqrt{15}}{-30}
$