7/5y-y=4

Solution for 7/5y-y=4 equation:

7/5y-y=4

We move all terms to the left:

7/5y-y-(4)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+7/5y-4=0

We multiply all the terms by the denominator


-1y*5y-4*5y+7=0

Wy multiply elements

-5y^2-20y+7=0

a = -5; b = -20; c = +7;
Δ = b2-4ac
Δ = -202-4·(-5)·7
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{15}}{2*-5}=\frac{20-6\sqrt{15}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{15}}{2*-5}=\frac{20+6\sqrt{15}}{-10}
$