2/5y-8y=-10

Solution for 2/5y-8y=-10 equation:

2/5y-8y=-10

We move all terms to the left:

2/5y-8y-(-10)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-8y+2/5y+10=0

We multiply all the terms by the denominator


-8y*5y+10*5y+2=0

Wy multiply elements

-40y^2+50y+2=0

a = -40; b = 50; c = +2;
Δ = b2-4ac
Δ = 502-4·(-40)·2
Δ = 2820
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:

$\sqrt{\Delta}=\sqrt{2820}=\sqrt{4*705}=\sqrt{4}*\sqrt{705}=2\sqrt{705}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{705}}{2*-40}=\frac{-50-2\sqrt{705}}{-80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{705}}{2*-40}=\frac{-50+2\sqrt{705}}{-80}
$