4(1/5y-1)=2/3y+17

Solution for 4(1/5y-1)=2/3y+17 equation:

4(1/5y-1)=2/3y+17

We move all terms to the left:

4(1/5y-1)-(2/3y+17)=0


Domain of the equation: 5y-1)!=0

y∈R



Domain of the equation: 3y+17)!=0

y∈R


We multiply parentheses

4y-(2/3y+17)-4=0

We get rid of parentheses

4y-2/3y-17-4=0

We multiply all the terms by the denominator


4y*3y-17*3y-4*3y-2=0

Wy multiply elements

12y^2-51y-12y-2=0

We add all the numbers together, and all the variables

12y^2-63y-2=0

a = 12; b = -63; c = -2;
Δ = b2-4ac
Δ = -632-4·12·(-2)
Δ = 4065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{4065}}{2*12}=\frac{63-\sqrt{4065}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4065}}{2*12}=\frac{63+\sqrt{4065}}{24}
$