(3/7)*y+(4/14)*y=10

Solution for (3/7)*y+(4/14)*y=10 equation:

(3/7)*y+(4/14)*y=10

We move all terms to the left:

(3/7)*y+(4/14)*y-(10)=0


Domain of the equation: 7)*y!=0

y!=0/1

y!=0

y∈R



Domain of the equation: 14)*y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+3/7)*y+(+4/14)*y-10=0

We multiply parentheses

3y^2+4y^2-10=0

We add all the numbers together, and all the variables

7y^2-10=0

a = 7; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·7·(-10)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*7}=\frac{0-2\sqrt{70}}{14}
=-\frac{2\sqrt{70}}{14}
=-\frac{\sqrt{70}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*7}=\frac{0+2\sqrt{70}}{14}
=\frac{2\sqrt{70}}{14}
=\frac{\sqrt{70}}{7}
$