1.5y-1y=4+1/2y

Solution for 1.5y-1y=4+1/2y equation:

1.5y-1y=4+1/2y

We move all terms to the left:

1.5y-1y-(4+1/2y)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1.5y-1y-(1/2y+4)=0

We add all the numbers together, and all the variables

0.5y-(1/2y+4)=0

We get rid of parentheses

0.5y-1/2y-4=0

We multiply all the terms by the denominator


(0.5y)*2y-4*2y-1=0

We add all the numbers together, and all the variables

(+0.5y)*2y-4*2y-1=0

We multiply parentheses

0y^2-4*2y-1=0

Wy multiply elements

0y^2-8y-1=0

We add all the numbers together, and all the variables

y^2-8y-1=0

a = 1; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·1·(-1)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{17}}{2*1}=\frac{8-2\sqrt{17}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{17}}{2*1}=\frac{8+2\sqrt{17}}{2}
$