y,-4/5y=12

Solution for y,-4/5y=12 equation:

y.-4/5y=12

We move all terms to the left:

y.-4/5y-(12)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We multiply all the terms by the denominator


(y.)*5y-12*5y-4=0

We add all the numbers together, and all the variables

(+y.)*5y-12*5y-4=0

We multiply parentheses

5y^2-12*5y-4=0

Wy multiply elements

5y^2-60y-4=0

a = 5; b = -60; c = -4;
Δ = b2-4ac
Δ = -602-4·5·(-4)
Δ = 3680
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:

$\sqrt{\Delta}=\sqrt{3680}=\sqrt{16*230}=\sqrt{16}*\sqrt{230}=4\sqrt{230}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{230}}{2*5}=\frac{60-4\sqrt{230}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{230}}{2*5}=\frac{60+4\sqrt{230}}{10}
$