94=5y(4y+2)

Solution for 94=5y(4y+2) equation:

94=5y(4y+2)

We move all terms to the left:

94-(5y(4y+2))=0


We calculate terms in parentheses: -(5y(4y+2)), so:

5y(4y+2)

We multiply parentheses

20y^2+10y

Back to the equation:

-(20y^2+10y)


We get rid of parentheses

-20y^2-10y+94=0

a = -20; b = -10; c = +94;
Δ = b2-4ac
Δ = -102-4·(-20)·94
Δ = 7620
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:

$\sqrt{\Delta}=\sqrt{7620}=\sqrt{4*1905}=\sqrt{4}*\sqrt{1905}=2\sqrt{1905}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1905}}{2*-20}=\frac{10-2\sqrt{1905}}{-40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1905}}{2*-20}=\frac{10+2\sqrt{1905}}{-40}
$