(5y+10)=(21/2y+15)

Solution for (5y+10)=(21/2y+15) equation:

(5y+10)=(21/2y+15)

We move all terms to the left:

(5y+10)-((21/2y+15))=0


Domain of the equation: 2y+15))!=0

y∈R


We get rid of parentheses

5y-((21/2y+15))+10=0

We multiply all the terms by the denominator


5y*2y+10*2y+15))-((21+15))=0

We add all the numbers together, and all the variables

5y*2y+10*2y+15))-(36)=0

We add all the numbers together, and all the variables

5y*2y+10*2y=0

Wy multiply elements

10y^2+20y=0

a = 10; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·10·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*10}=\frac{-40}{20}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*10}=\frac{0}{20}
=0
$