y-4/5y=14

Solution for y-4/5y=14 equation:

y-4/5y=14

We move all terms to the left:

y-4/5y-(14)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We multiply all the terms by the denominator


y*5y-14*5y-4=0

Wy multiply elements

5y^2-70y-4=0

a = 5; b = -70; c = -4;
Δ = b2-4ac
Δ = -702-4·5·(-4)
Δ = 4980
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:

$\sqrt{\Delta}=\sqrt{4980}=\sqrt{4*1245}=\sqrt{4}*\sqrt{1245}=2\sqrt{1245}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1245}}{2*5}=\frac{70-2\sqrt{1245}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1245}}{2*5}=\frac{70+2\sqrt{1245}}{10}
$