810=((760/y-1)+14)*(y-5)

Solution for 810=((760/y-1)+14)*(y-5) equation:

810=((760/y-1)+14)(y-5)

We move all terms to the left:

810-(((760/y-1)+14)(y-5))=0


Domain of the equation: y-1)+14)(y-5))!=0

y∈R


We multiply all the terms by the denominator


-(((760+810*y-1)+14)(y-5))=0


We calculate terms in parentheses: -(((760+810*y-1)+14)(y-5)), so:

((760+810*y-1)+14)(y-5)

We add all the numbers together, and all the variables

((810y+759)+14)(y-5)


We calculate terms in parentheses: +((810y+759)+14)(y-5), so:

(810y+759)+14)(y-5

We get rid of parentheses

810y+14)(y+759-5

We add all the numbers together, and all the variables

810y+14)(y+754

Back to the equation:

+(810y+14)(y+754)


We multiply parentheses ..

(+810y^2+610740y+14y+10556)

We get rid of parentheses

810y^2+610740y+14y+10556

We add all the numbers together, and all the variables

810y^2+610754y+10556

Back to the equation:

-(810y^2+610754y+10556)


We get rid of parentheses

-810y^2-610754y-10556=0

a = -810; b = -610754; c = -10556;
Δ = b2-4ac
Δ = -6107542-4·(-810)·(-10556)
Δ = 372986247076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{372986247076}=610726$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-610754)-610726}{2*-810}=\frac{28}{-1620}
=-7/405
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-610754)+610726}{2*-810}=\frac{1221480}{-1620}
=-754
$