y=5/7y+200

Solution for y=5/7y+200 equation:

y=5/7y+200

We move all terms to the left:

y-(5/7y+200)=0


Domain of the equation: 7y+200)!=0

y∈R


We get rid of parentheses

y-5/7y-200=0

We multiply all the terms by the denominator


y*7y-200*7y-5=0

Wy multiply elements

7y^2-1400y-5=0

a = 7; b = -1400; c = -5;
Δ = b2-4ac
Δ = -14002-4·7·(-5)
Δ = 1960140
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:

$\sqrt{\Delta}=\sqrt{1960140}=\sqrt{4*490035}=\sqrt{4}*\sqrt{490035}=2\sqrt{490035}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1400)-2\sqrt{490035}}{2*7}=\frac{1400-2\sqrt{490035}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1400)+2\sqrt{490035}}{2*7}=\frac{1400+2\sqrt{490035}}{14}
$