y-3/2y+1=4

Solution for y-3/2y+1=4 equation:

y-3/2y+1=4

We move all terms to the left:

y-3/2y+1-(4)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y-3/2y-3=0

We multiply all the terms by the denominator


y*2y-3*2y-3=0

Wy multiply elements

2y^2-6y-3=0

a = 2; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·2·(-3)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*2}=\frac{6-2\sqrt{15}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*2}=\frac{6+2\sqrt{15}}{4}
$