6/5*y=42

Solution for 6/5*y=42 equation:

6/5*y=42

We move all terms to the left:

6/5*y-(42)=0


Domain of the equation: 5*y!=0

y!=0/1

y!=0

y∈R


We multiply all the terms by the denominator


-42*5*y+6=0

Wy multiply elements

-210y*y+6=0

Wy multiply elements

-210y^2+6=0

a = -210; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-210)·6
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{35}}{2*-210}=\frac{0-12\sqrt{35}}{-420}
=-\frac{12\sqrt{35}}{-420}
=-\frac{\sqrt{35}}{-35}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{35}}{2*-210}=\frac{0+12\sqrt{35}}{-420}
=\frac{12\sqrt{35}}{-420}
=\frac{\sqrt{35}}{-35}
$