(1/3)x+(2/3)x=262

Solution for (1/3)x+(2/3)x=262 equation:

(1/3)x+(2/3)x=262

We move all terms to the left:

(1/3)x+(2/3)x-(262)=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

(+1/3)x+(+2/3)x-262=0

We multiply parentheses

x^2+2x^2-262=0

We add all the numbers together, and all the variables

3x^2-262=0

a = 3; b = 0; c = -262;
Δ = b2-4ac
Δ = 02-4·3·(-262)
Δ = 3144
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:

$\sqrt{\Delta}=\sqrt{3144}=\sqrt{4*786}=\sqrt{4}*\sqrt{786}=2\sqrt{786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{786}}{2*3}=\frac{0-2\sqrt{786}}{6}
=-\frac{2\sqrt{786}}{6}
=-\frac{\sqrt{786}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{786}}{2*3}=\frac{0+2\sqrt{786}}{6}
=\frac{2\sqrt{786}}{6}
=\frac{\sqrt{786}}{3}
$