5y(6-2y)=-(19-18y)

Solution for 5y(6-2y)=-(19-18y) equation:

5y(6-2y)=-(19-18y)

We move all terms to the left:

5y(6-2y)-(-(19-18y))=0

We add all the numbers together, and all the variables

5y(-2y+6)-(-(-18y+19))=0

We multiply parentheses

-10y^2+30y-(-(-18y+19))=0


We calculate terms in parentheses: -(-(-18y+19)), so:

-(-18y+19)

We get rid of parentheses

18y-19

Back to the equation:

-(18y-19)


We get rid of parentheses

-10y^2+30y-18y+19=0

We add all the numbers together, and all the variables

-10y^2+12y+19=0

a = -10; b = 12; c = +19;
Δ = b2-4ac
Δ = 122-4·(-10)·19
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{226}}{2*-10}=\frac{-12-2\sqrt{226}}{-20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{226}}{2*-10}=\frac{-12+2\sqrt{226}}{-20}
$