4/5y-2=-9/10y+30

Solution for 4/5y-2=-9/10y+30 equation:

4/5y-2=-9/10y+30

We move all terms to the left:

4/5y-2-(-9/10y+30)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 10y+30)!=0

y∈R


We get rid of parentheses

4/5y+9/10y-30-2=0

We calculate fractions


40y/50y^2+45y/50y^2-30-2=0

We add all the numbers together, and all the variables

40y/50y^2+45y/50y^2-32=0

We multiply all the terms by the denominator


40y+45y-32*50y^2=0

We add all the numbers together, and all the variables

85y-32*50y^2=0

Wy multiply elements

-1600y^2+85y=0

a = -1600; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-1600)·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*-1600}=\frac{-170}{-3200}
=17/320
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-1600}=\frac{0}{-3200}
=0
$