3(1/2y+5)=4(3/7y-8)

Solution for 3(1/2y+5)=4(3/7y-8) equation:

3(1/2y+5)=4(3/7y-8)

We move all terms to the left:

3(1/2y+5)-(4(3/7y-8))=0


Domain of the equation: 2y+5)!=0

y∈R



Domain of the equation: 7y-8))!=0

y∈R


We multiply parentheses

3y-(4(3/7y-8))+15=0

We multiply all the terms by the denominator


3y*7y+15*7y-8))-(4(3-8))=0

We add all the numbers together, and all the variables

3y*7y+15*7y-8))-(4(-5))=0

We add all the numbers together, and all the variables

3y*7y+15*7y=0

Wy multiply elements

21y^2+105y=0

a = 21; b = 105; c = 0;
Δ = b2-4ac
Δ = 1052-4·21·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-105}{2*21}=\frac{-210}{42}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+105}{2*21}=\frac{0}{42}
=0
$