5-y=7.5-11/4y

Solution for 5-y=7.5-11/4y equation:

5-y=7.5-11/4y

We move all terms to the left:

5-y-(7.5-11/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-y-(-11/4y+7.5)+5=0

We add all the numbers together, and all the variables

-1y-(-11/4y+7.5)+5=0

We get rid of parentheses

-1y+11/4y-7.5+5=0

We multiply all the terms by the denominator


-1y*4y-(7.5)*4y+5*4y+11=0

We multiply parentheses

-1y*4y-30y+5*4y+11=0

Wy multiply elements

-4y^2-30y+20y+11=0

We add all the numbers together, and all the variables

-4y^2-10y+11=0

a = -4; b = -10; c = +11;
Δ = b2-4ac
Δ = -102-4·(-4)·11
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{69}}{2*-4}=\frac{10-2\sqrt{69}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{69}}{2*-4}=\frac{10+2\sqrt{69}}{-8}
$