0.5y+4=5/1.2y+8=3

Solution for 0.5y+4=5/1.2y+8=3 equation:

0.5y+4=5/1.2y+8=3

We move all terms to the left:

0.5y+4-(5/1.2y+8)=0


Domain of the equation: 1.2y+8)!=0

y∈R


We get rid of parentheses

0.5y-5/1.2y-8+4=0

We multiply all the terms by the denominator


(0.5y)*1.2y-8*1.2y+4*1.2y-5=0

We add all the numbers together, and all the variables

(+0.5y)*1.2y-8*1.2y+4*1.2y-5=0

We multiply parentheses

0y^2-8*1.2y+4*1.2y-5=0

Wy multiply elements

0y^2-8y+4y-5=0

We add all the numbers together, and all the variables

y^2-4y-5=0

a = 1; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·1·(-5)
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{-(-4)-6}{2*1}=\frac{-2}{2}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*1}=\frac{10}{2}
=5
$