(1/2)y+(1/3)y=10

Solution for (1/2)y+(1/3)y=10 equation:

(1/2)y+(1/3)y=10

We move all terms to the left:

(1/2)y+(1/3)y-(10)=0


Domain of the equation: 2)y!=0

y!=0/1

y!=0

y∈R



Domain of the equation: 3)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+1/2)y+(+1/3)y-10=0

We multiply parentheses

y^2+y^2-10=0

We add all the numbers together, and all the variables

2y^2-10=0

a = 2; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·2·(-10)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*2}=\frac{0-4\sqrt{5}}{4}
=-\frac{4\sqrt{5}}{4}
=-\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*2}=\frac{0+4\sqrt{5}}{4}
=\frac{4\sqrt{5}}{4}
=\sqrt{5}
$