5/2*y=12

Solution for 5/2*y=12 equation:

5/2*y=12

We move all terms to the left:

5/2*y-(12)=0


Domain of the equation: 2*y!=0

y!=0/1

y!=0

y∈R


We multiply all the terms by the denominator


-12*2*y+5=0

Wy multiply elements

-24y*y+5=0

Wy multiply elements

-24y^2+5=0

a = -24; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-24)·5
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-24}=\frac{0-4\sqrt{30}}{-48}
=-\frac{4\sqrt{30}}{-48}
=-\frac{\sqrt{30}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-24}=\frac{0+4\sqrt{30}}{-48}
=\frac{4\sqrt{30}}{-48}
=\frac{\sqrt{30}}{-12}
$