2/5y-8=9y+2

Solution for 2/5y-8=9y+2 equation:

2/5y-8=9y+2

We move all terms to the left:

2/5y-8-(9y+2)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We get rid of parentheses

2/5y-9y-2-8=0

We multiply all the terms by the denominator


-9y*5y-2*5y-8*5y+2=0

Wy multiply elements

-45y^2-10y-40y+2=0

We add all the numbers together, and all the variables

-45y^2-50y+2=0

a = -45; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·(-45)·2
Δ = 2860
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:

$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{715}}{2*-45}=\frac{50-2\sqrt{715}}{-90}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{715}}{2*-45}=\frac{50+2\sqrt{715}}{-90}
$