6/5(y)=6y+28

Solution for 6/5(y)=6y+28 equation:

6/5(y)=6y+28

We move all terms to the left:

6/5(y)-(6y+28)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We get rid of parentheses

6/5y-6y-28=0

We multiply all the terms by the denominator


-6y*5y-28*5y+6=0

Wy multiply elements

-30y^2-140y+6=0

a = -30; b = -140; c = +6;
Δ = b2-4ac
Δ = -1402-4·(-30)·6
Δ = 20320
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:

$\sqrt{\Delta}=\sqrt{20320}=\sqrt{16*1270}=\sqrt{16}*\sqrt{1270}=4\sqrt{1270}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1270}}{2*-30}=\frac{140-4\sqrt{1270}}{-60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1270}}{2*-30}=\frac{140+4\sqrt{1270}}{-60}
$