4(1/3)x=260

Solution for 4(1/3)x=260 equation:

4(1/3)x=260

We move all terms to the left:

4(1/3)x-(260)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(+1/3)x-260=0

We multiply parentheses

4x^2-260=0

a = 4; b = 0; c = -260;
Δ = b2-4ac
Δ = 02-4·4·(-260)
Δ = 4160
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:

$\sqrt{\Delta}=\sqrt{4160}=\sqrt{64*65}=\sqrt{64}*\sqrt{65}=8\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{65}}{2*4}=\frac{0-8\sqrt{65}}{8}
=-\frac{8\sqrt{65}}{8}
=-\sqrt{65}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{65}}{2*4}=\frac{0+8\sqrt{65}}{8}
=\frac{8\sqrt{65}}{8}
=\sqrt{65}
$