174=y(80-y/5)

Solution for 174=y(80-y/5) equation:

174=y(80-y/5)

We move all terms to the left:

174-(y(80-y/5))=0

We add all the numbers together, and all the variables

-(y(-y/5+80))+174=0

We multiply all the terms by the denominator


-(y(-y+174*5+80))=0


We calculate terms in parentheses: -(y(-y+174*5+80)), so:

y(-y+174*5+80)

We add all the numbers together, and all the variables

y(-1y+950)

We multiply parentheses

-1y^2+950y

Back to the equation:

-(-1y^2+950y)


We get rid of parentheses

1y^2-950y=0

We add all the numbers together, and all the variables

y^2-950y=0

a = 1; b = -950; c = 0;
Δ = b2-4ac
Δ = -9502-4·1·0
Δ = 902500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{902500}=950$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-950)-950}{2*1}=\frac{0}{2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-950)+950}{2*1}=\frac{1900}{2}
=950
$