3/2y-y=10

Solution for 3/2y-y=10 equation:

3/2y-y=10

We move all terms to the left:

3/2y-y-(10)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+3/2y-10=0

We multiply all the terms by the denominator


-1y*2y-10*2y+3=0

Wy multiply elements

-2y^2-20y+3=0

a = -2; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-2)·3
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*-2}=\frac{20-2\sqrt{106}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*-2}=\frac{20+2\sqrt{106}}{-4}
$