3/2y=-2y+13

Solution for 3/2y=-2y+13 equation:

3/2y=-2y+13

We move all terms to the left:

3/2y-(-2y+13)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

3/2y+2y-13=0

We multiply all the terms by the denominator


2y*2y-13*2y+3=0

Wy multiply elements

4y^2-26y+3=0

a = 4; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·4·3
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{157}}{2*4}=\frac{26-2\sqrt{157}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{157}}{2*4}=\frac{26+2\sqrt{157}}{8}
$