4/5y-1=-9/10y+4

Solution for 4/5y-1=-9/10y+4 equation:

4/5y-1=-9/10y+4

We move all terms to the left:

4/5y-1-(-9/10y+4)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+4)!=0

y∈R


We get rid of parentheses

4/5y+9/10y-4-1=0

We calculate fractions


40y/50y^2+45y/50y^2-4-1=0

We add all the numbers together, and all the variables

40y/50y^2+45y/50y^2-5=0

We multiply all the terms by the denominator


40y+45y-5*50y^2=0

We add all the numbers together, and all the variables

85y-5*50y^2=0

Wy multiply elements

-250y^2+85y=0

a = -250; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-250)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-250}=\frac{-170}{-500}
=17/50
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-250}=\frac{0}{-500}
=0
$