1.52y=3.17y(y-8.57)

Solution for 1.52y=3.17y(y-8.57) equation:

1.52y=3.17y(y-8.57)

We move all terms to the left:

1.52y-(3.17y(y-8.57))=0


We calculate terms in parentheses: -(3.17y(y-8.57)), so:

3.17y(y-8.57)

We multiply parentheses

3y^2-25.71y

Back to the equation:

-(3y^2-25.71y)


We get rid of parentheses

-3y^2+1.52y+25.71y=0

We add all the numbers together, and all the variables

-3y^2+27.23y=0

a = -3; b = 27.23; c = 0;
Δ = b2-4ac
Δ = 27.232-4·(-3)·0
Δ = 741.4729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27.23)-\sqrt{741.4729}}{2*-3}=\frac{-27.23-\sqrt{741.4729}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27.23)+\sqrt{741.4729}}{2*-3}=\frac{-27.23+\sqrt{741.4729}}{-6}
$