7/2y+4/3y=5

Solution for 7/2y+4/3y=5 equation:

7/2y+4/3y=5

We move all terms to the left:

7/2y+4/3y-(5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We calculate fractions


21y/6y^2+8y/6y^2-5=0

We multiply all the terms by the denominator


21y+8y-5*6y^2=0

We add all the numbers together, and all the variables

29y-5*6y^2=0

Wy multiply elements

-30y^2+29y=0

a = -30; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-30)·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*-30}=\frac{-58}{-60}
=29/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-30}=\frac{0}{-60}
=0
$