4.5y-2=3/10y+1

Solution for 4.5y-2=3/10y+1 equation:

4.5y-2=3/10y+1

We move all terms to the left:

4.5y-2-(3/10y+1)=0


Domain of the equation: 10y+1)!=0

y∈R


We get rid of parentheses

4.5y-3/10y-1-2=0

We multiply all the terms by the denominator


(4.5y)*10y-1*10y-2*10y-3=0

We add all the numbers together, and all the variables

(+4.5y)*10y-1*10y-2*10y-3=0

We multiply parentheses

40y^2-1*10y-2*10y-3=0

Wy multiply elements

40y^2-10y-20y-3=0

We add all the numbers together, and all the variables

40y^2-30y-3=0

a = 40; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·40·(-3)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{345}}{2*40}=\frac{30-2\sqrt{345}}{80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{345}}{2*40}=\frac{30+2\sqrt{345}}{80}
$