5(2.2y+3.4)=5y(y-2)+6y

Solution for 5(2.2y+3.4)=5y(y-2)+6y equation:

5(2.2y+3.4)=5y(y-2)+6y

We move all terms to the left:

5(2.2y+3.4)-(5y(y-2)+6y)=0

We multiply parentheses

10y-(5y(y-2)+6y)+17=0


We calculate terms in parentheses: -(5y(y-2)+6y), so:

5y(y-2)+6y

We add all the numbers together, and all the variables

6y+5y(y-2)

We multiply parentheses

5y^2+6y-10y

We add all the numbers together, and all the variables

5y^2-4y

Back to the equation:

-(5y^2-4y)


We get rid of parentheses

-5y^2+10y+4y+17=0

We add all the numbers together, and all the variables

-5y^2+14y+17=0

a = -5; b = 14; c = +17;
Δ = b2-4ac
Δ = 142-4·(-5)·17
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{134}}{2*-5}=\frac{-14-2\sqrt{134}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{134}}{2*-5}=\frac{-14+2\sqrt{134}}{-10}
$