-1/5y+8=3/4y-11

Solution for -1/5y+8=3/4y-11 equation:

-1/5y+8=3/4y-11

We move all terms to the left:

-1/5y+8-(3/4y-11)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 4y-11)!=0

y∈R


We get rid of parentheses

-1/5y-3/4y+11+8=0

We calculate fractions


(-4y)/20y^2+(-15y)/20y^2+11+8=0

We add all the numbers together, and all the variables

(-4y)/20y^2+(-15y)/20y^2+19=0

We multiply all the terms by the denominator


(-4y)+(-15y)+19*20y^2=0

Wy multiply elements

380y^2+(-4y)+(-15y)=0

We get rid of parentheses

380y^2-4y-15y=0

We add all the numbers together, and all the variables

380y^2-19y=0

a = 380; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·380·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*380}=\frac{0}{760}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*380}=\frac{38}{760}
=1/20
$