3y-30+1=5/2y-20

Solution for 3y-30+1=5/2y-20 equation:

3y-30+1=5/2y-20

We move all terms to the left:

3y-30+1-(5/2y-20)=0


Domain of the equation: 2y-20)!=0

y∈R


We add all the numbers together, and all the variables

3y-(5/2y-20)-29=0

We get rid of parentheses

3y-5/2y+20-29=0

We multiply all the terms by the denominator


3y*2y+20*2y-29*2y-5=0

Wy multiply elements

6y^2+40y-58y-5=0

We add all the numbers together, and all the variables

6y^2-18y-5=0

a = 6; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·6·(-5)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*6}=\frac{18-2\sqrt{111}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*6}=\frac{18+2\sqrt{111}}{12}
$