5/4y-1+7/3y-2=180

Solution for 5/4y-1+7/3y-2=180 equation:

5/4y-1+7/3y-2=180

We move all terms to the left:

5/4y-1+7/3y-2-(180)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

5/4y+7/3y-183=0

We calculate fractions


15y/12y^2+28y/12y^2-183=0

We multiply all the terms by the denominator


15y+28y-183*12y^2=0

We add all the numbers together, and all the variables

43y-183*12y^2=0

Wy multiply elements

-2196y^2+43y=0

a = -2196; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-2196)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-2196}=\frac{-86}{-4392}
=43/2196
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-2196}=\frac{0}{-4392}
=0
$