3/2y+4/7y=10

Solution for 3/2y+4/7y=10 equation:

3/2y+4/7y=10

We move all terms to the left:

3/2y+4/7y-(10)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We calculate fractions


21y/14y^2+8y/14y^2-10=0

We multiply all the terms by the denominator


21y+8y-10*14y^2=0

We add all the numbers together, and all the variables

29y-10*14y^2=0

Wy multiply elements

-140y^2+29y=0

a = -140; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-140)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-140}=\frac{-58}{-280}
=29/140
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-140}=\frac{0}{-280}
=0
$