-1/4y+15=2/5y-11

Solution for -1/4y+15=2/5y-11 equation:

-1/4y+15=2/5y-11

We move all terms to the left:

-1/4y+15-(2/5y-11)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 5y-11)!=0

y∈R


We get rid of parentheses

-1/4y-2/5y+11+15=0

We calculate fractions


(-5y)/20y^2+(-8y)/20y^2+11+15=0

We add all the numbers together, and all the variables

(-5y)/20y^2+(-8y)/20y^2+26=0

We multiply all the terms by the denominator


(-5y)+(-8y)+26*20y^2=0

Wy multiply elements

520y^2+(-5y)+(-8y)=0

We get rid of parentheses

520y^2-5y-8y=0

We add all the numbers together, and all the variables

520y^2-13y=0

a = 520; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·520·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*520}=\frac{0}{1040}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*520}=\frac{26}{1040}
=1/40
$