6.5y-19=2.5y(y-4)

Solution for 6.5y-19=2.5y(y-4) equation:

6.5y-19=2.5y(y-4)

We move all terms to the left:

6.5y-19-(2.5y(y-4))=0


We calculate terms in parentheses: -(2.5y(y-4)), so:

2.5y(y-4)

We multiply parentheses

2y^2-8y

Back to the equation:

-(2y^2-8y)


We get rid of parentheses

-2y^2+6.5y+8y-19=0

We add all the numbers together, and all the variables

-2y^2+14.5y-19=0

a = -2; b = 14.5; c = -19;
Δ = b2-4ac
Δ = 14.52-4·(-2)·(-19)
Δ = 58.25
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{-(14.5)-\sqrt{58.25}}{2*-2}=\frac{-14.5-\sqrt{58.25}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14.5)+\sqrt{58.25}}{2*-2}=\frac{-14.5+\sqrt{58.25}}{-4}
$