Y/5y-3=2y+7

Solution for Y/5y-3=2y+7 equation:

/5Y-3=2Y+7

We move all terms to the left:

/5Y-3-(2Y+7)=0


Domain of the equation: 5Y!=0

Y!=0/5

Y!=0

Y∈R


We get rid of parentheses

/5Y-2Y-7-3=0

We multiply all the terms by the denominator


-2Y*5Y-7*5Y-3*5Y+=0

We add all the numbers together, and all the variables

-2Y*5Y-7*5Y-3*5Y=0

Wy multiply elements

-10Y^2-35Y-15Y=0

We add all the numbers together, and all the variables

-10Y^2-50Y=0

a = -10; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-10)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-10}=\frac{0}{-20}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-10}=\frac{100}{-20}
=-5
$