5/4y-3y=-33

Solution for 5/4y-3y=-33 equation:

5/4y-3y=-33

We move all terms to the left:

5/4y-3y-(-33)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-3y+5/4y+33=0

We multiply all the terms by the denominator


-3y*4y+33*4y+5=0

Wy multiply elements

-12y^2+132y+5=0

a = -12; b = 132; c = +5;
Δ = b2-4ac
Δ = 1322-4·(-12)·5
Δ = 17664
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:

$\sqrt{\Delta}=\sqrt{17664}=\sqrt{256*69}=\sqrt{256}*\sqrt{69}=16\sqrt{69}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-16\sqrt{69}}{2*-12}=\frac{-132-16\sqrt{69}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+16\sqrt{69}}{2*-12}=\frac{-132+16\sqrt{69}}{-24}
$