4/5y+20=5y-22

Solution for 4/5y+20=5y-22 equation:

4/5y+20=5y-22

We move all terms to the left:

4/5y+20-(5y-22)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We get rid of parentheses

4/5y-5y+22+20=0

We multiply all the terms by the denominator


-5y*5y+22*5y+20*5y+4=0

Wy multiply elements

-25y^2+110y+100y+4=0

We add all the numbers together, and all the variables

-25y^2+210y+4=0

a = -25; b = 210; c = +4;
Δ = b2-4ac
Δ = 2102-4·(-25)·4
Δ = 44500
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:

$\sqrt{\Delta}=\sqrt{44500}=\sqrt{100*445}=\sqrt{100}*\sqrt{445}=10\sqrt{445}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-10\sqrt{445}}{2*-25}=\frac{-210-10\sqrt{445}}{-50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+10\sqrt{445}}{2*-25}=\frac{-210+10\sqrt{445}}{-50}
$