4/5y-3y=-32

Solution for 4/5y-3y=-32 equation:

4/5y-3y=-32

We move all terms to the left:

4/5y-3y-(-32)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-3y+4/5y+32=0

We multiply all the terms by the denominator


-3y*5y+32*5y+4=0

Wy multiply elements

-15y^2+160y+4=0

a = -15; b = 160; c = +4;
Δ = b2-4ac
Δ = 1602-4·(-15)·4
Δ = 25840
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:

$\sqrt{\Delta}=\sqrt{25840}=\sqrt{16*1615}=\sqrt{16}*\sqrt{1615}=4\sqrt{1615}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-4\sqrt{1615}}{2*-15}=\frac{-160-4\sqrt{1615}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+4\sqrt{1615}}{2*-15}=\frac{-160+4\sqrt{1615}}{-30}
$