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

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

3/7y+4/14y=10

We move all terms to the left:

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


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 14y!=0

y!=0/14

y!=0

y∈R


We calculate fractions


42y/98y^2+28y/98y^2-10=0

We multiply all the terms by the denominator


42y+28y-10*98y^2=0

We add all the numbers together, and all the variables

70y-10*98y^2=0

Wy multiply elements

-980y^2+70y=0

a = -980; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-980)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-980}=\frac{-140}{-1960}
=1/14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-980}=\frac{0}{-1960}
=0
$