(1/2)x+(2/3)x=105

Solution for (1/2)x+(2/3)x=105 equation:

(1/2)x+(2/3)x=105

We move all terms to the left:

(1/2)x+(2/3)x-(105)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x+(+2/3)x-105=0

We multiply parentheses

x^2+2x^2-105=0

We add all the numbers together, and all the variables

3x^2-105=0

a = 3; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·3·(-105)
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*3}=\frac{0-6\sqrt{35}}{6}
=-\frac{6\sqrt{35}}{6}
=-\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*3}=\frac{0+6\sqrt{35}}{6}
=\frac{6\sqrt{35}}{6}
=\sqrt{35}
$