1/2y+3/4y=24

Solution for 1/2y+3/4y=24 equation:

1/2y+3/4y=24

We move all terms to the left:

1/2y+3/4y-(24)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


4y/8y^2+6y/8y^2-24=0

We multiply all the terms by the denominator


4y+6y-24*8y^2=0

We add all the numbers together, and all the variables

10y-24*8y^2=0

Wy multiply elements

-192y^2+10y=0

a = -192; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-192)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-192}=\frac{-20}{-384}
=5/96
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-192}=\frac{0}{-384}
=0
$