6y-3=6(1/2y-4)

Solution for 6y-3=6(1/2y-4) equation:

6y-3=6(1/2y-4)

We move all terms to the left:

6y-3-(6(1/2y-4))=0


Domain of the equation: 2y-4))!=0

y∈R


We multiply all the terms by the denominator


6y*2y-3*2y-4))-(6(1-4))=0

We add all the numbers together, and all the variables

6y*2y-3*2y-4))-(6(-3))=0

We add all the numbers together, and all the variables

6y*2y-3*2y=0

Wy multiply elements

12y^2-6y=0

a = 12; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·12·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*12}=\frac{0}{24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*12}=\frac{12}{24}
=1/2
$