-3=12y-5y(2y-7)

Solution for -3=12y-5y(2y-7) equation:

-3=12y-5y(2y-7)

We move all terms to the left:

-3-(12y-5y(2y-7))=0


We calculate terms in parentheses: -(12y-5y(2y-7)), so:

12y-5y(2y-7)

We multiply parentheses

-10y^2+12y+35y

We add all the numbers together, and all the variables

-10y^2+47y

Back to the equation:

-(-10y^2+47y)


We get rid of parentheses

10y^2-47y-3=0

a = 10; b = -47; c = -3;
Δ = b2-4ac
Δ = -472-4·10·(-3)
Δ = 2329
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{-(-47)-\sqrt{2329}}{2*10}=\frac{47-\sqrt{2329}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2329}}{2*10}=\frac{47+\sqrt{2329}}{20}
$